{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T01:22:12Z","timestamp":1783041732984,"version":"3.54.6"},"reference-count":44,"publisher":"American Mathematical Society (AMS)","issue":"324","license":[{"start":{"date-parts":[[2020,12,26]],"date-time":"2020-12-26T00:00:00Z","timestamp":1608940800000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1913080"],"award-info":[{"award-number":["1913080"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["11771338"],"award-info":[{"award-number":["11771338"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["2019110066"],"award-info":[{"award-number":["2019110066"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["LY17A010010"],"award-info":[{"award-number":["LY17A010010"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["1913080"],"award-info":[{"award-number":["1913080"]}],"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":["11771338"],"award-info":[{"award-number":["11771338"]}],"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":["2019110066"],"award-info":[{"award-number":["2019110066"]}],"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":["LY17A010010"],"award-info":[{"award-number":["LY17A010010"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["1913080"],"award-info":[{"award-number":["1913080"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["11771338"],"award-info":[{"award-number":["11771338"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["2019110066"],"award-info":[{"award-number":["2019110066"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["LY17A010010"],"award-info":[{"award-number":["LY17A010010"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["1913080"],"award-info":[{"award-number":["1913080"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["11771338"],"award-info":[{"award-number":["11771338"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["2019110066"],"award-info":[{"award-number":["2019110066"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY17A010010"],"award-info":[{"award-number":["LY17A010010"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A unified construction of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript m\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -nonconforming virtual elements of any order\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k\">\n                        <mml:semantics>\n                          <mml:mi>k<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">k<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    is developed on any shape of polytope in\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"double-struck upper R Superscript n\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                              <mml:mi mathvariant=\"double-struck\">R<\/mml:mi>\n                            <\/mml:mrow>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">\\mathbb {R}^n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    with constraints\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m less-than-or-equal-to n\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>m<\/mml:mi>\n                            <mml:mo>\n                              \u2264\n                              \n                            <\/mml:mo>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">m\\leq n<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    and\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"k greater-than-or-equal-to m\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>k<\/mml:mi>\n                            <mml:mo>\n                              \u2265\n                              \n                            <\/mml:mo>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">k\\geq m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . As a vital tool in the construction, a generalized Green\u2019s identity for\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript m\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    inner product is derived. The\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript m\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -nonconforming virtual element methods are then used to approximate solutions of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"m\">\n                        <mml:semantics>\n                          <mml:mi>m<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -harmonic equation. After establishing a bound on the jump related to the weak continuity, the optimal error estimate of the canonical interpolation, and the norm equivalence of the stabilization term, the optimal error estimates are derived for the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper H Superscript m\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>H<\/mml:mi>\n                            <mml:mi>m<\/mml:mi>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">H^m<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -nonconforming virtual element methods.\n                  <\/p>","DOI":"10.1090\/mcom\/3498","type":"journal-article","created":{"date-parts":[[2019,10,30]],"date-time":"2019-10-30T14:54:37Z","timestamp":1572447277000},"page":"1711-1744","source":"Crossref","is-referenced-by-count":60,"title":["Nonconforming Virtual Element Method for 2\ud835\udc5ath Order Partial Differential Equations in \u211d\u207f"],"prefix":"10.1090","volume":"89","author":[{"given":"Long","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuehai","family":"Huang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2019,12,26]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics (Amsterdam)","isbn-type":"print","volume-title":"Sobolev spaces","volume":"140","author":"Adams, Robert A.","year":"2003","ISBN":"https:\/\/id.crossref.org\/isbn\/0120441438","edition":"2"},{"key":"2","doi-asserted-by":"publisher","first-page":"623","DOI":"10.1002\/cpa.3160120405","article-title":"Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I","volume":"12","author":"Agmon, S.","year":"1959","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"issue":"3","key":"3","doi-asserted-by":"publisher","first-page":"376","DOI":"10.1016\/j.camwa.2013.05.015","article-title":"Equivalent projectors for virtual element methods","volume":"66","author":"Ahmad, B.","year":"2013","journal-title":"Comput. Math. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0898-1221","issn-type":"print"},{"issue":"195","key":"4","doi-asserted-by":"publisher","first-page":"299","DOI":"10.2307\/2938675","article-title":"The structure of multivariate superspline spaces of high degree","volume":"57","author":"Alfeld, Peter","year":"1991","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"387","DOI":"10.1142\/S0218202518500100","article-title":"The fully nonconforming virtual element method for biharmonic problems","volume":"28","author":"Antonietti, P. F.","year":"2018","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"key":"6","doi-asserted-by":"crossref","unstructured":"P. F. Antonietti, G. Manzini, and M. Verani, The conforming virtual element method for polyharmonic problems, Comput. Math. Appl., 2019. \\url{https:\/\/doi.org\/10.1016\/j.camwa.2019.09.022.}","DOI":"10.2172\/1475305"},{"key":"7","doi-asserted-by":"crossref","unstructured":"J. Argyris, I. Fried, and D. Scharpf, The TUBA family of plate elements for the matrix displacement method, The Aeronautical Journal of the Royal Aeronautical Society 72 (1968), 701\u2013709.","DOI":"10.1017\/S000192400008489X"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"879","DOI":"10.1051\/m2an\/2015090","article-title":"The nonconforming virtual element method","volume":"50","author":"Ayuso de Dios, Blanca","year":"2016","journal-title":"ESAIM Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/2822-7840","issn-type":"print"},{"key":"9","doi-asserted-by":"crossref","unstructured":"I. Babu\u0161ka, Error-bounds for finite element method, Numer. Math. 16 (1971), 322\u2013333.","DOI":"10.1007\/BF02165003"},{"issue":"3","key":"10","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1007\/s00211-017-0921-7","article-title":"Exponential convergence of the \u210e\ud835\udc5d virtual element method in presence of corner singularities","volume":"138","author":"Beir\u00e3o da Veiga, L.","year":"2018","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"5","key":"11","doi-asserted-by":"publisher","first-page":"1110","DOI":"10.1016\/j.camwa.2017.03.021","article-title":"High-order virtual element method on polyhedral meshes","volume":"74","author":"Beir\u00e3o da Veiga, L.","year":"2017","journal-title":"Comput. Math. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0898-1221","issn-type":"print"},{"issue":"1","key":"12","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1142\/S0218202512500492","article-title":"Basic principles of virtual element methods","volume":"23","author":"Beir\u00e3o da Veiga, L.","year":"2013","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"8","key":"13","doi-asserted-by":"publisher","first-page":"1541","DOI":"10.1142\/S021820251440003X","article-title":"The hitchhiker\u2019s guide to the virtual element method","volume":"24","author":"Beir\u00e3o da Veiga, L.","year":"2014","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"13","key":"14","doi-asserted-by":"publisher","first-page":"2557","DOI":"10.1142\/S021820251750052X","article-title":"Stability analysis for the virtual element method","volume":"27","author":"Beir\u00e3o da Veiga, Louren\u00e7o","year":"2017","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"key":"15","doi-asserted-by":"publisher","first-page":"809","DOI":"10.2307\/2004615","article-title":"Triangular elements in the finite element method","volume":"24","author":"Bramble, James H.","year":"1970","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"16","series-title":"Texts in Applied Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-75934-0","volume-title":"The mathematical theory of finite element methods","volume":"15","author":"Brenner, Susanne C.","year":"2008","ISBN":"https:\/\/id.crossref.org\/isbn\/9780387759333","edition":"3"},{"issue":"7","key":"17","doi-asserted-by":"publisher","first-page":"1291","DOI":"10.1142\/S0218202518500355","article-title":"Virtual element methods on meshes with small edges or faces","volume":"28","author":"Brenner, Susanne C.","year":"2018","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"2","key":"18","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1051\/m2an:2008046","article-title":"Mimetic finite differences for elliptic problems","volume":"43","author":"Brezzi, Franco","year":"2009","journal-title":"M2AN Math. Model. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0764-583X","issn-type":"print"},{"key":"19","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1016\/j.cma.2012.09.012","article-title":"Virtual element methods for plate bending problems","volume":"253","author":"Brezzi, Franco","year":"2013","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"5","key":"20","doi-asserted-by":"publisher","first-page":"2913","DOI":"10.1137\/17M1154369","article-title":"Anisotropic error estimates of the linear virtual element method on polygonal meshes","volume":"56","author":"Cao, Shuhao","year":"2018","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"3","key":"21","doi-asserted-by":"publisher","first-page":"1058","DOI":"10.1137\/18M1196455","article-title":"Anisotropic error estimates of the linear nonconforming virtual element methods","volume":"57","author":"Cao, Shuhao","year":"2019","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"1","key":"22","doi-asserted-by":"publisher","first-page":"Paper No. 5, 23","DOI":"10.1007\/s10092-018-0249-4","article-title":"Some error analysis on virtual element methods","volume":"55","author":"Chen, Long","year":"2018","journal-title":"Calcolo","ISSN":"https:\/\/id.crossref.org\/issn\/0008-0624","issn-type":"print"},{"key":"23","series-title":"Studies in Mathematics and its Applications, Vol. 4","isbn-type":"print","volume-title":"The finite element method for elliptic problems","author":"Ciarlet, Philippe G.","year":"1978","ISBN":"https:\/\/id.crossref.org\/isbn\/0444850287"},{"issue":"9","key":"24","doi-asserted-by":"publisher","first-page":"3379","DOI":"10.1016\/j.camwa.2018.02.005","article-title":"Exploring high-order three dimensional virtual elements: bases and stabilizations","volume":"75","author":"Dassi, F.","year":"2018","journal-title":"Comput. Math. Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0898-1221","issn-type":"print"},{"key":"25","isbn-type":"print","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03286-2","volume-title":"Mathematical theory of elastic structures","author":"Feng, Kang","year":"1996","ISBN":"https:\/\/id.crossref.org\/isbn\/3540513264"},{"key":"26","series-title":"Lecture Notes in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-12245-3","volume-title":"Polyharmonic boundary value problems","volume":"1991","author":"Gazzola, Filippo","year":"2010","ISBN":"https:\/\/id.crossref.org\/isbn\/9783642122446"},{"issue":"4","key":"27","doi-asserted-by":"publisher","first-page":"1350","DOI":"10.1137\/100806497","article-title":"The lowest order differentiable finite element on rectangular grids","volume":"49","author":"Hu, Jun","year":"2011","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"4","key":"28","doi-asserted-by":"publisher","first-page":"731","DOI":"10.1007\/s00211-012-0445-0","article-title":"Convergence and optimality of the adaptive Morley element method","volume":"121","author":"Hu, Jun","year":"2012","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"292","key":"29","doi-asserted-by":"publisher","first-page":"563","DOI":"10.1090\/S0025-5718-2014-02871-8","article-title":"The minimal conforming \ud835\udc3b^{\ud835\udc58} finite element spaces on \ud835\udc45\u207f rectangular grids","volume":"84","author":"Hu, Jun","year":"2015","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"30","first-page":"266","article-title":"A canonical construction of \ud835\udc3b^{\ud835\udc5a}-nonconforming triangular finite elements","volume":"33","author":"Hu, Jun","year":"2017","journal-title":"Ann. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/2096-0174","issn-type":"print"},{"issue":"1","key":"31","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/s10915-018-0780-0","article-title":"A hybridizable discontinuous Galerkin method for Kirchhoff plates","volume":"78","author":"Huang, Jianguo","year":"2019","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"},{"key":"32","doi-asserted-by":"publisher","first-page":"694","DOI":"10.1016\/j.cma.2017.03.027","article-title":"A nonconforming virtual element method for the Stokes problem on general meshes","volume":"320","author":"Liu, Xin","year":"2017","journal-title":"Comput. Methods Appl. Mech. Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/0045-7825","issn-type":"print"},{"issue":"4","key":"33","doi-asserted-by":"publisher","first-page":"1258","DOI":"10.1002\/num.22257","article-title":"Ill-conditioning in the virtual element method: stabilizations and bases","volume":"34","author":"Mascotto, Lorenzo","year":"2018","journal-title":"Numer. Methods Partial Differential Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0749-159X","issn-type":"print"},{"key":"34","doi-asserted-by":"crossref","unstructured":"J. N. Reddy, Theory and Analysis of Elastic Plates and Shells, CRC Press, New York, second edition, 2006.","DOI":"10.1201\/9780849384165"},{"key":"35","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/BF02165119","article-title":"Interpolation polynomials on the triangle","volume":"15","author":"\u017den\u00ed\u0161ek, Alexander","year":"1970","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"1","key":"36","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1007\/s00211-005-0662-x","article-title":"The Morley element for fourth order elliptic equations in any dimensions","volume":"103","author":"Wang, Ming","year":"2006","journal-title":"Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0029-599X","issn-type":"print"},{"issue":"281","key":"37","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1090\/S0025-5718-2012-02611-1","article-title":"Minimal finite element spaces for 2\ud835\udc5a-th-order partial differential equations in \ud835\udc45\u207f","volume":"82","author":"Wang, Ming","year":"2013","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"315","key":"38","doi-asserted-by":"publisher","first-page":"237","DOI":"10.1090\/mcom\/3334","article-title":"A nonconforming Crouzeix-Raviart type finite element on polygonal meshes","volume":"88","author":"Wang, Yanqiu","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"39","unstructured":"S. Wu and J. Xu, \ud835\udcab\u2098 interior penalty nonconforming finite element methods for 2\ud835\udcc2-th order PDEs in \u211b\u207f, arXiv:1710.07678, 2017."},{"issue":"316","key":"40","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1090\/mcom\/3361","article-title":"Nonconforming finite element spaces for 2\ud835\udc5ath order partial differential equations on \u211d\u207f simplicial grids when \ud835\udd5e=\ud835\udd5f+1","volume":"88","author":"Wu, Shuonan","year":"2019","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"1","key":"41","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/j.apnum.2008.02.002","article-title":"A family of 3D continuously differentiable finite elements on tetrahedral grids","volume":"59","author":"Zhang, Shangyou","year":"2009","journal-title":"Appl. Numer. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0168-9274","issn-type":"print"},{"issue":"6","key":"42","doi-asserted-by":"publisher","first-page":"701","DOI":"10.4208\/aamm.09-m0993","article-title":"On the full \ud835\udc36\u2081-\ud835\udc44_{\ud835\udc58} finite element spaces on rectangles and cuboids","volume":"2","author":"Zhang, Shangyou","year":"2010","journal-title":"Adv. Appl. Math. Mech.","ISSN":"https:\/\/id.crossref.org\/issn\/2070-0733","issn-type":"print"},{"issue":"9","key":"43","doi-asserted-by":"publisher","first-page":"1671","DOI":"10.1142\/S021820251650041X","article-title":"The nonconforming virtual element method for plate bending problems","volume":"26","author":"Zhao, Jikun","year":"2016","journal-title":"Math. Models Methods Appl. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-2025","issn-type":"print"},{"issue":"1","key":"44","doi-asserted-by":"publisher","first-page":"610","DOI":"10.1007\/s10915-017-0632-3","article-title":"The Morley-type virtual element for plate bending problems","volume":"76","author":"Zhao, Jikun","year":"2018","journal-title":"J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0885-7474","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/mcom\/2020-89-324\/S0025-5718-2019-03498-1\/mcom3498_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"http:\/\/www.ams.org\/mcom\/0000-000-00\/S0025-5718-2019-03498-1\/S0025-5718-2019-03498-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2020-89-324\/S0025-5718-2019-03498-1\/S0025-5718-2019-03498-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T03:41:41Z","timestamp":1776829301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2020-89-324\/S0025-5718-2019-03498-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12,26]]},"references-count":44,"journal-issue":{"issue":"324","published-print":{"date-parts":[[2020,7]]}},"alternative-id":["S0025-5718-2019-03498-1"],"URL":"https:\/\/doi.org\/10.1090\/mcom\/3498","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2019,12,26]]}}}