{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T20:56:08Z","timestamp":1777755368181,"version":"3.51.4"},"reference-count":34,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11625101"],"award-info":[{"award-number":["11625101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11421101"],"award-info":[{"award-number":["11421101"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>A conforming triangular mixed element recently proposed by Hu and Zhang for linear elasticity is extended by rearranging the global degrees of freedom.\nMore precisely, adaptive meshes <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9999\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:msub>\n                              <m:mo>,<\/m:mo>\n                              <m:mi mathvariant=\"normal\">\u2026<\/m:mi>\n                              <m:mo>,<\/m:mo>\n                              <m:msub>\n                                 <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                                 <m:mi>N<\/m:mi>\n                              <\/m:msub>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0358.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{1},\\ldots,\\mathcal{T}_{N}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> which are successively refined from an initial mesh <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9998\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mn>0<\/m:mn>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0357.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{0}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> through a newest vertex bisection strategy, admit a crucial hierarchical structure, namely, a newly added vertex <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9997\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of the mesh <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9996\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0361.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{\\ell}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is the midpoint of an edge <jats:italic>e<\/jats:italic> of the coarse mesh <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9995\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mrow>\n                                 <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                                 <m:mo>-<\/m:mo>\n                                 <m:mn>1<\/m:mn>\n                              <\/m:mrow>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0360.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{\\ell-1}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nSuch a hierarchical structure is explored to partially relax the <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9994\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msup>\n                              <m:mi>C<\/m:mi>\n                              <m:mn>0<\/m:mn>\n                           <\/m:msup>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0178.png\"\/>\n                        <jats:tex-math>{C^{0}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> vertex continuity of symmetric matrix-valued functions in the discrete stress space of the original element on <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9993\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0361.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{\\ell}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and results in an extended discrete stress space: for such an internal vertex <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9992\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> located at the coarse edge <jats:italic>e<\/jats:italic> with the unit tangential vector <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9991\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>t<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0523.png\"\/>\n                        <jats:tex-math>{t_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and the unit normal vector <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9990\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>n<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>=<\/m:mo>\n                              <m:msubsup>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                                 <m:mo>\u22a5<\/m:mo>\n                              <\/m:msubsup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0505.png\"\/>\n                        <jats:tex-math>{n_{e}=t_{e}^{\\perp}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, the pure tangential component basis function <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9989\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msub>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msubsup>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                                 <m:mi>T<\/m:mi>\n                              <\/m:msubsup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0432.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}(\\boldsymbol{x})t_{e}t_{e}^{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of the original discrete stress space associated to vertex <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9988\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is split into two basis functions <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9987\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msubsup>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>+<\/m:mo>\n                              <\/m:msubsup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msub>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msubsup>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                                 <m:mi>T<\/m:mi>\n                              <\/m:msubsup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0435.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}^{+}(\\boldsymbol{x})t_{e}t_{e}^{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9986\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msubsup>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>-<\/m:mo>\n                              <\/m:msubsup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msub>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msubsup>\n                                 <m:mi>t<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                                 <m:mi>T<\/m:mi>\n                              <\/m:msubsup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0437.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}^{-}(\\boldsymbol{x})t_{e}t_{e}^{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> along edge <jats:italic>e<\/jats:italic>, where <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9985\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0433.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}(\\boldsymbol{x})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is the nodal basis function of the scalar-valued Lagrange element of order <jats:italic>k<\/jats:italic> (<jats:italic>k<\/jats:italic> is equal to the polynomial degree of the discrete stress) on <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9984\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0361.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{\\ell}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> with <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9983\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msubsup>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>+<\/m:mo>\n                              <\/m:msubsup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0436.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}^{+}(\\boldsymbol{x})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> and <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9982\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msubsup>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                                 <m:mo>-<\/m:mo>\n                              <\/m:msubsup>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0438.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}^{-}(\\boldsymbol{x})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> denoted its two restrictions on two sides of <jats:italic>e<\/jats:italic>, respectively.\nSince the remaining two basis functions <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9981\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msub>\n                                 <m:mi>n<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:msubsup>\n                                 <m:mi>n<\/m:mi>\n                                 <m:mi>e<\/m:mi>\n                                 <m:mi>T<\/m:mi>\n                              <\/m:msubsup>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0431.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}(\\boldsymbol{x})n_{e}n_{e}^{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9980\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:msub>\n                                 <m:mi>\u03c6<\/m:mi>\n                                 <m:msub>\n                                    <m:mi>\ud835\udc99<\/m:mi>\n                                    <m:mi>e<\/m:mi>\n                                 <\/m:msub>\n                              <\/m:msub>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>\ud835\udc99<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mrow>\n                                    <m:mrow>\n                                       <m:msub>\n                                          <m:mi>n<\/m:mi>\n                                          <m:mi>e<\/m:mi>\n                                       <\/m:msub>\n                                       <m:mo>\u2062<\/m:mo>\n                                       <m:msubsup>\n                                          <m:mi>t<\/m:mi>\n                                          <m:mi>e<\/m:mi>\n                                          <m:mi>T<\/m:mi>\n                                       <\/m:msubsup>\n                                    <\/m:mrow>\n                                    <m:mo>+<\/m:mo>\n                                    <m:mrow>\n                                       <m:msub>\n                                          <m:mi>t<\/m:mi>\n                                          <m:mi>e<\/m:mi>\n                                       <\/m:msub>\n                                       <m:mo>\u2062<\/m:mo>\n                                       <m:msubsup>\n                                          <m:mi>n<\/m:mi>\n                                          <m:mi>e<\/m:mi>\n                                          <m:mi>T<\/m:mi>\n                                       <\/m:msubsup>\n                                    <\/m:mrow>\n                                 <\/m:mrow>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0430.png\"\/>\n                        <jats:tex-math>{\\varphi_{\\boldsymbol{x}_{e}}(\\boldsymbol{x})(n_{e}t_{e}^{T}+t_{e}n_{e}^{T})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> are the same as those associated to <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9979\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of the original discrete stress space, the number of the global basis functions associated to <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9978\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of the extended discrete stress space becomes four rather than three (for the original discrete stress space).\nAs a result, though the extended discrete stress space on <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9977\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mi mathvariant=\"normal\">\u2113<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0361.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}_{\\ell}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is still a <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9976\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>H<\/m:mi>\n                              <m:mo>\u2062<\/m:mo>\n                              <m:mrow>\n                                 <m:mo stretchy=\"false\">(<\/m:mo>\n                                 <m:mi>div<\/m:mi>\n                                 <m:mo stretchy=\"false\">)<\/m:mo>\n                              <\/m:mrow>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0197.png\"\/>\n                        <jats:tex-math>{H(\\operatorname{div})}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> subspace, the pure tangential component along the coarse edge <jats:italic>e<\/jats:italic> of discrete stresses in it is not necessarily continuous at such vertices like <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9975\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:msub>\n                              <m:mi>\ud835\udc99<\/m:mi>\n                              <m:mi>e<\/m:mi>\n                           <\/m:msub>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0292.png\"\/>\n                        <jats:tex-math>{\\boldsymbol{x}_{e}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>.\nA feature of this extended discrete stress space is its nestedness in the sense that a space on a coarse mesh <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9974\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0362.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> is a subspace of a space on any refinement <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9973\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mover accent=\"true\">\n                              <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                              <m:mo stretchy=\"false\">^<\/m:mo>\n                           <\/m:mover>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0313.png\"\/>\n                        <jats:tex-math>{\\hat{\\mathcal{T}}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula> of <jats:inline-formula id=\"j_cmam-2020-0003_ineq_9972\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mi mathvariant=\"script\">\ud835\udcaf<\/m:mi>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2020-0003_eq_0362.png\"\/>\n                        <jats:tex-math>{\\mathcal{T}}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, which allows a proof of convergence of a standard adaptive algorithm.\nThe idea is extended to impose a general traction boundary condition on the discrete level.\nNumerical experiments are provided to illustrate performance on both uniform and adaptive meshes.<\/jats:p>","DOI":"10.1515\/cmam-2020-0003","type":"journal-article","created":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T09:00:57Z","timestamp":1590656457000},"page":"89-108","source":"Crossref","is-referenced-by-count":3,"title":["Partial Relaxation of \ud835\udc36<sup>0<\/sup> Vertex Continuity of Stresses of Conforming Mixed Finite Elements for the Elasticity Problem"],"prefix":"10.1515","volume":"21","author":[{"given":"Jun","family":"Hu","sequence":"first","affiliation":[{"name":"LMAM and School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Ma","sequence":"additional","affiliation":[{"name":"LMAM and School of Mathematical Sciences , Peking University , Beijing 100871 , P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2020,5,27]]},"reference":[{"key":"2023033111222119870_j_cmam-2020-0003_ref_001","doi-asserted-by":"crossref","unstructured":"S.  Adams and B.  Cockburn,\nA mixed finite element method for elasticity in three dimensions,\nJ. Sci. Comput. 25 (2005), no. 3, 515\u2013521.","DOI":"10.1007\/s10915-004-4807-3"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_002","unstructured":"D. N.  Arnold,\nDifferential complexes and numerical stability,\nProceedings of the ICM, Vol. I: Plenary Lectures and Ceremonies,\nHigher Education Press, Beijing (2002), 137\u2013157."},{"key":"2023033111222119870_j_cmam-2020-0003_ref_003","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold and G.  Awanou,\nRectangular mixed finite elements for elasticity,\nMath. Models Methods Appl. Sci. 15 (2005), no. 9, 1417\u20131429.","DOI":"10.1142\/S0218202505000741"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_004","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold, G.  Awanou and R.  Winther,\nFinite elements for symmetric tensors in three dimensions,\nMath. Comp. 77 (2008), no. 263, 1229\u20131251.","DOI":"10.1090\/S0025-5718-08-02071-1"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_005","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold, F.  Brezzi and J.  Douglas, Jr.,\nPEERS: A new mixed finite element for plane elasticity,\nJapan J. Appl. Math. 1 (1984), no. 2, 347\u2013367.","DOI":"10.1007\/BF03167064"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_006","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold, R. S.  Falk and R.  Winther,\nMixed finite element methods for linear elasticity with weakly imposed symmetry,\nMath. Comp. 76 (2007), no. 260, 1699\u20131723.","DOI":"10.1090\/S0025-5718-07-01998-9"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_007","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold and R.  Winther,\nMixed finite elements for elasticity,\nNumer. Math. 92 (2002), no. 3, 401\u2013419.","DOI":"10.1007\/s002110100348"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_008","doi-asserted-by":"crossref","unstructured":"R.  Becker and S.  Mao,\nAn optimally convergent adaptive mixed finite element method,\nNumer. Math. 111 (2008), no. 1, 35\u201354.","DOI":"10.1007\/s00211-008-0180-8"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_009","doi-asserted-by":"crossref","unstructured":"D.  Boffi, F.  Brezzi and M.  Fortin,\nReduced symmetry elements in linear elasticity,\nCommun. Pure Appl. Anal. 8 (2009), no. 1, 95\u2013121.","DOI":"10.3934\/cpaa.2009.8.95"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_010","doi-asserted-by":"crossref","unstructured":"D.  Boffi, F.  Brezzi and M.  Fortin,\nMixed Finite Element Methods and Applications,\nSpringer Ser. Comput. Math. 44,\nSpringer, Heidelberg, 2013.","DOI":"10.1007\/978-3-642-36519-5"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_011","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, M.  Feischl, M.  Page and D.  Praetorius,\nAxioms of adaptivity,\nComput. Math. Appl. 67 (2014), no. 6, 1195\u20131253.","DOI":"10.1016\/j.camwa.2013.12.003"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_012","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, D.  Gallistl and J.  Gedicke,\nResidual-based a posteriori error analysis for symmetric mixed Arnold\u2013Winther FEM,\nNumer. Math. 142 (2019), no. 2, 205\u2013234.","DOI":"10.1007\/s00211-019-01029-7"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_013","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, D.  Gallistl and M.  Schedensack,\n\n                  \n                     \n                        \n                           L\n                           2\n                        \n                     \n                     \n                     L^{2}\n                  \n                best approximation of the elastic stress in the Arnold\u2013Winther FEM,\nIMA J. Numer. Anal. 36 (2016), no. 3, 1096\u20131119.","DOI":"10.1093\/imanum\/drv051"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_014","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and J.  Gedicke,\nRobust residual-based a posteriori Arnold\u2013Winther mixed finite element analysis in elasticity,\nComput. Methods Appl. Mech. Engrg. 300 (2016), 245\u2013264.","DOI":"10.1016\/j.cma.2015.10.001"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_015","doi-asserted-by":"crossref","unstructured":"C.  Carstensen, D.  G\u00fcnther, J.  Reininghaus and J.  Thiele,\nThe Arnold\u2013Winther mixed FEM in linear elasticity. I. Implementation and numerical verification,\nComput. Methods Appl. Mech. Engrg. 197 (2008), no. 33\u201340, 3014\u20133023.","DOI":"10.1016\/j.cma.2008.02.005"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_016","doi-asserted-by":"crossref","unstructured":"C.  Carstensen and R. H. W.  Hoppe,\nError reduction and convergence for an adaptive mixed finite element method,\nMath. Comp. 75 (2006), no. 255, 1033\u20131042.","DOI":"10.1090\/S0025-5718-06-01829-1"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_017","unstructured":"C.  Carstensen and J.  Hu,\nAn extended Argyris finite element method with optimal standard adaptive and multigrid V-cycle algorithms, preprint (2019)."},{"key":"2023033111222119870_j_cmam-2020-0003_ref_018","doi-asserted-by":"crossref","unstructured":"J. M.  Cascon, C.  Kreuzer, R. H.  Nochetto and K. G.  Siebert,\nQuasi-optimal convergence rate for an adaptive finite element method,\nSIAM J. Numer. Anal. 46 (2008), no. 5, 2524\u20132550.","DOI":"10.1137\/07069047X"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_019","doi-asserted-by":"crossref","unstructured":"L.  Chen, M.  Holst and J.  Xu,\nConvergence and optimality of adaptive mixed finite element methods,\nMath. Comp. 78 (2009), no. 265, 35\u201353.","DOI":"10.1090\/S0025-5718-08-02155-8"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_020","doi-asserted-by":"crossref","unstructured":"L.  Chen, J.  Hu and X.  Huang,\nFast auxiliary space preconditioner for linear elasticity in mixed form,\nMath. Comp. 87 (2018), no. 312, 1601\u20131633.","DOI":"10.1090\/mcom\/3285"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_021","doi-asserted-by":"crossref","unstructured":"L.  Chen, J.  Hu, X.  Huang and H.  Man,\nResidual-based a posteriori error estimates for symmetric conforming mixed finite elements for linear elasticity problems,\nSci. China Math. 61 (2018), no. 6, 973\u2013992.","DOI":"10.1007\/s11425-017-9181-2"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_022","doi-asserted-by":"crossref","unstructured":"V.  Girault and L. R.  Scott,\nHermite interpolation of nonsmooth functions preserving boundary conditions,\nMath. Comp. 71 (2002), no. 239, 1043\u20131074.","DOI":"10.1090\/S0025-5718-02-01446-1"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_023","doi-asserted-by":"crossref","unstructured":"H. C.  Hu,\nOn some variational principles in the theory of elasticity and the theory of plasticity,\nActa Phys. Sin. 10 (1954), no. 3, 259\u2013290.","DOI":"10.7498\/aps.10.259"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_024","doi-asserted-by":"crossref","unstructured":"J.  Hu,\nA new family of efficient conforming mixed finite elements on both rectangular and cuboid meshes for linear elasticity in the symmetric formulation,\nSIAM J. Numer. Anal. 53 (2015), no. 3, 1438\u20131463.","DOI":"10.1137\/130945272"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_025","doi-asserted-by":"crossref","unstructured":"J.  Hu,\nFinite element approximations of symmetric tensors on simplicial grids in \n                  \n                     \n                        \n                           \u211d\n                           n\n                        \n                     \n                     \n                     \\mathbb{R}^{n}\n                  \n               : The higher order case,\nJ. Comput. Math. 33 (2015), no. 3, 283\u2013296.","DOI":"10.4208\/jcm.1412-m2014-0071"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_026","doi-asserted-by":"crossref","unstructured":"J.  Hu and G.  Yu,\nA unified analysis of quasi-optimal convergence for adaptive mixed finite element methods,\nSIAM J. Numer. Anal. 56 (2018), no. 1, 296\u2013316.","DOI":"10.1137\/16M105513X"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_027","unstructured":"J.  Hu and S.  Zhang,\nA family of conforming mixed finite elements for linear elasticity on triangular grids, preprint (2014), https:\/\/arxiv.org\/abs\/1406.7457."},{"key":"2023033111222119870_j_cmam-2020-0003_ref_028","doi-asserted-by":"crossref","unstructured":"J.  Hu and S.  Zhang,\nA family of symmetric mixed finite elements for linear elasticity on tetrahedral grids,\nSci. China Math. 58 (2015), no. 2, 297\u2013307.","DOI":"10.1007\/s11425-014-4953-5"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_029","doi-asserted-by":"crossref","unstructured":"J.  Hu and S.  Zhang,\nFinite element approximations of symmetric tensors on simplicial grids in \n                  \n                     \n                        \n                           \u211d\n                           n\n                        \n                     \n                     \n                     \\mathbb{R}^{n}\n                  \n               : The lower order case,\nMath. Models Methods Appl. Sci. 26 (2016), no. 9, 1649\u20131669.","DOI":"10.1142\/S0218202516500408"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_030","doi-asserted-by":"crossref","unstructured":"J.  Huang, X.  Huang and Y.  Xu,\nConvergence of an adaptive mixed finite element method for Kirchhoff plate bending problems,\nSIAM J. Numer. Anal. 49 (2011), no. 2, 574\u2013607.","DOI":"10.1137\/090773374"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_031","doi-asserted-by":"crossref","unstructured":"J.  Huang and Y.  Xu,\nConvergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation,\nSci. China Math. 55 (2012), no. 5, 1083\u20131098.","DOI":"10.1007\/s11425-012-4384-0"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_032","doi-asserted-by":"crossref","unstructured":"C.  Johnson and B.  Mercier,\nSome equilibrium finite element methods for two-dimensional elasticity problems,\nNumer. Math. 30 (1978), no. 1, 103\u2013116.","DOI":"10.1007\/BF01403910"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_033","doi-asserted-by":"crossref","unstructured":"R.  Stevenson,\nThe completion of locally refined simplicial partitions created by bisection,\nMath. Comp. 77 (2008), no. 261, 227\u2013241.","DOI":"10.1090\/S0025-5718-07-01959-X"},{"key":"2023033111222119870_j_cmam-2020-0003_ref_034","doi-asserted-by":"crossref","unstructured":"X.  Zhao, J.  Hu and Z.  Shi,\nConvergence analysis of the adaptive finite element method with the red-green refinement,\nSci. China Math. 53 (2010), no. 2, 499\u2013512.","DOI":"10.1007\/s11425-009-0200-x"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/21\/1\/article-p89.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0003\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0003\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T14:34:39Z","timestamp":1680273279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2020-0003\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,27]]},"references-count":34,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,2,7]]},"published-print":{"date-parts":[[2021,1,1]]}},"alternative-id":["10.1515\/cmam-2020-0003"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2020-0003","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,27]]}}}