{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:40:11Z","timestamp":1680262811112},"reference-count":16,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771312","11401407","91430105"],"award-info":[{"award-number":["11771312","11401407","91430105"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The embedded discontinuous Galerkin (EDG) method by Cockburn, Gopalakrishnan and Lazarov [B. Cockburn, J. Gopalakrishnan and R. Lazarov,\nUnified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second-order elliptic problems,\nSIAM J. Numer. Anal. 47 2009, 2, 1319\u20131365]\nis obtained from the hybridizable discontinuous Galerkin method by changing the space of the Lagrangian multiplier from discontinuous\nfunctions to continuous ones, and adopts piecewise polynomials of equal degrees on simplex meshes for all variables.\nIn this paper, we analyze a new EDG method for second-order elliptic problems on polygonal\/polyhedral meshes. By using piecewise polynomials of degrees <jats:inline-formula id=\"j_cmam-2018-0007_ineq_9999_w2aab3b7d297b1b6b1aab1c14b1b1Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>k<\/m:mi>\n                              <m:mo>+<\/m:mo>\n                              <m:mn>1<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2018-0007_eq_0638.png\" \/>\n                        <jats:tex-math>{k+1}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, <jats:inline-formula id=\"j_cmam-2018-0007_ineq_9998_w2aab3b7d297b1b6b1aab1c14b1b3Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>k<\/m:mi>\n                              <m:mo>+<\/m:mo>\n                              <m:mn>1<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2018-0007_eq_0638.png\" \/>\n                        <jats:tex-math>{k+1}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>, <jats:italic>k<\/jats:italic> (<jats:inline-formula id=\"j_cmam-2018-0007_ineq_9997_w2aab3b7d297b1b6b1aab1c14b1b7Aa\">\n                     <jats:alternatives>\n                        <m:math xmlns:m=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                           <m:mrow>\n                              <m:mi>k<\/m:mi>\n                              <m:mo>\u2265<\/m:mo>\n                              <m:mn>0<\/m:mn>\n                           <\/m:mrow>\n                        <\/m:math>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/j_cmam-2018-0007_eq_0640.png\" \/>\n                        <jats:tex-math>{k\\geq 0}<\/jats:tex-math>\n                     <\/jats:alternatives>\n                  <\/jats:inline-formula>) to approximate the potential, numerical trace and flux, respectively, the new method is shown to yield optimal convergence rates for both the potential and flux approximations. Numerical experiments are provided to confirm the theoretical results.<\/jats:p>","DOI":"10.1515\/cmam-2018-0007","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T08:24:53Z","timestamp":1523521493000},"page":"849-861","source":"Crossref","is-referenced-by-count":2,"title":["An Optimal Embedded Discontinuous Galerkin Method for Second-Order Elliptic Problems"],"prefix":"10.1515","volume":"19","author":[{"given":"Xiao","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics , Sichuan University , Chengdu 610064 , P. R. China"}]},{"given":"Xiaoping","family":"Xie","sequence":"additional","affiliation":[{"name":"School of Mathematics , Sichuan University , Chengdu 610064 , P. R. China"}]},{"given":"Shiquan","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics , Sichuan University , Chengdu 610064 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2018,3,20]]},"reference":[{"key":"2023033110105322680_j_cmam-2018-0007_ref_001_w2aab3b7d297b1b6b1ab2ab1Aa","doi-asserted-by":"crossref","unstructured":"D. N.  Arnold, F.  Brezzi, B.  Cockburn and L. D.  Marini,\nUnified analysis of discontinuous Galerkin methods for elliptic problems,\nSIAM J. Numer. Anal. 39 (2001\/02), no. 5, 1749\u20131779.","DOI":"10.1137\/S0036142901384162"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_002_w2aab3b7d297b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"F.  Brezzi, J.  Douglas, Jr. and L. D.  Marini,\nTwo families of mixed finite elements for second order elliptic problems,\nNumer. Math. 47 (1985), no. 2, 217\u2013235.","DOI":"10.1007\/BF01389710"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_003_w2aab3b7d297b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn and J.  Gopalakrishnan,\nA characterization of hybridized mixed methods for second order elliptic problems,\nSIAM J. Numer. Anal. 42 (2004), no. 1, 283\u2013301.","DOI":"10.1137\/S0036142902417893"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_004_w2aab3b7d297b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn, J.  Gopalakrishnan and R.  Lazarov,\nUnified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems,\nSIAM J. Numer. Anal. 47 (2009), no. 2, 1319\u20131365.","DOI":"10.1137\/070706616"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_005_w2aab3b7d297b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn, J.  Gopalakrishnan and F.-J.  Sayas,\nA projection-based error analysis of HDG methods,\nMath. Comp. 79 (2010), no. 271, 1351\u20131367.","DOI":"10.1090\/S0025-5718-10-02334-3"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_006_w2aab3b7d297b1b6b1ab2ab6Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn, J.  Gopalakrishnan and H.  Wang,\nLocally conservative fluxes for the continuous Galerkin method,\nSIAM J. Numer. Anal. 45 (2007), no. 4, 1742\u20131776.","DOI":"10.1137\/060666305"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_007_w2aab3b7d297b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn, J.  Guzm\u00e1n, S.-C.  Soon and H. K.  Stolarski,\nAn analysis of the embedded discontinuous Galerkin method for second-order elliptic problems,\nSIAM J. Numer. Anal. 47 (2009), no. 4, 2686\u20132707.","DOI":"10.1137\/080726914"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_008_w2aab3b7d297b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"B.  Cockburn, W.  Qiu and K.  Shi,\nConditions for superconvergence of HDG methods for second-order elliptic problems,\nMath. Comp. 81 (2012), no. 279, 1327\u20131353.","DOI":"10.1090\/S0025-5718-2011-02550-0"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_009_w2aab3b7d297b1b6b1ab2ab9Aa","doi-asserted-by":"crossref","unstructured":"P.  Fernandez, N. C.  Nguyen and X.  Roca,\nImplicit large-eddy simulation of compressible flows using the interior embedded discontinuous Galerkin method,\nAIAA Sci. Tech. Forum (2016), https:\/\/doi.org\/10.2514\/6.2016-1332.","DOI":"10.2514\/6.2016-1332"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_010_w2aab3b7d297b1b6b1ab2ac10Aa","unstructured":"C.  Gang and X.  Xie,\nRobust weak Galerkin finite element methods for linear elasticity with continuous displacement trace approximation,\npreprint (2017), https:\/\/arxiv.org\/abs\/1710.07905."},{"key":"2023033110105322680_j_cmam-2018-0007_ref_011_w2aab3b7d297b1b6b1ab2ac11Aa","doi-asserted-by":"crossref","unstructured":"S.  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Forum (2013), https:\/\/doi.org\/10.2514\/6.2011-3228.","DOI":"10.2514\/6.2011-3228"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_014_w2aab3b7d297b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"N. C.  Nguyen, J.  Peraire and B.  Cockburn,\nA class of embedded discontinuous Galerkin methods for computational fluid dynamics,\nJ. Comput. Phys. 302 (2015), 674\u2013692.","DOI":"10.1016\/j.jcp.2015.09.024"},{"key":"2023033110105322680_j_cmam-2018-0007_ref_015_w2aab3b7d297b1b6b1ab2ac15Aa","unstructured":"Z.  Shi and M.  Wang,\nFinite Element Methods,\nScience Press, Beijing, 2013."},{"key":"2023033110105322680_j_cmam-2018-0007_ref_016_w2aab3b7d297b1b6b1ab2ac16Aa","unstructured":"G.  Vacca,\nAdvancements in mimetic and virtual element methods,\nPh.D. thesis, Universit\u00e0 Degli Studi Di Bar, 2016."}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/19\/4\/article-p849.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0007\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0007\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:20:40Z","timestamp":1680261640000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0007\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,20]]},"references-count":16,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4,10]]},"published-print":{"date-parts":[[2019,10,1]]}},"alternative-id":["10.1515\/cmam-2018-0007"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0007","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2018,3,20]]}}}