{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:37:41Z","timestamp":1776847061102,"version":"3.51.2"},"reference-count":59,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-1418934"],"award-info":[{"award-number":["DMS-1418934"]}],"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":["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":["11271035"],"award-info":[{"award-number":["11271035"]}],"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":["91430213"],"award-info":[{"award-number":["91430213"]}],"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"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11301396"],"award-info":[{"award-number":["11301396"]}],"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":["11671304"],"award-info":[{"award-number":["11671304"]}],"id":[{"id":"10.13039\/501100001809","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"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY15A010015"],"award-info":[{"award-number":["LY15A010015"]}],"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":["LY15A010016"],"award-info":[{"award-number":["LY15A010016"]}],"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":["LY14A010020"],"award-info":[{"award-number":["LY14A010020"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2017,1,1]]},"abstract":"Abstract<\/jats:title>\n In this paper, we design two classes of stabilized mixed finite element methods for linear elasticity on simplicial grids.\nIn the first class of elements, we use \n \n \n \n \ud835\udc6f<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n div<\/m:mo>\n ,<\/m:mo>\n \u03a9<\/m:mi>\n ;<\/m:mo>\n \ud835\udd4a<\/m:mi>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n ${\\boldsymbol{H}(\\operatorname{div},\\Omega;\\mathbb{S})}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-\n \n \n \n P<\/m:mi>\n k<\/m:mi>\n <\/m:msub>\n <\/m:math>\n ${P_{k}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> and \n \n \n \n \n \ud835\udc73<\/m:mi>\n 2<\/m:mn>\n <\/m:msup>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \u03a9<\/m:mi>\n ;<\/m:mo>\n \n \u211d<\/m:mi>\n n<\/m:mi>\n <\/m:msup>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n ${\\boldsymbol{L}^{2}(\\Omega;\\mathbb{R}^{n})}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-\n \n \n \n P<\/m:mi>\n \n k<\/m:mi>\n -<\/m:mo>\n 1<\/m:mn>\n <\/m:mrow>\n <\/m:msub>\n <\/m:math>\n ${P_{k-1}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> to approximate the stress and displacement spaces, respectively, for \n \n \n \n 1<\/m:mn>\n \u2264<\/m:mo>\n k<\/m:mi>\n \u2264<\/m:mo>\n n<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n ${1\\leq k\\leq n}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, and employ a stabilization technique in terms of\nthe jump of the discrete displacement over the edges\/faces of the triangulation under consideration; in the second class of elements, we use \n \n \n \n \n \ud835\udc6f<\/m:mi>\n 0<\/m:mn>\n 1<\/m:mn>\n <\/m:msubsup>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n \u03a9<\/m:mi>\n ;<\/m:mo>\n \n \u211d<\/m:mi>\n n<\/m:mi>\n <\/m:msup>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n ${\\boldsymbol{H}_{0}^{1}(\\Omega;\\mathbb{R}^{n})}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>-\n \n \n \n P<\/m:mi>\n k<\/m:mi>\n <\/m:msub>\n <\/m:math>\n ${P_{k}}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> to approximate the displacement space for \n \n \n \n 1<\/m:mn>\n \u2264<\/m:mo>\n k<\/m:mi>\n \u2264<\/m:mo>\n n<\/m:mi>\n <\/m:mrow>\n <\/m:math>\n ${1\\leq k\\leq n}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, and adopt the stabilization technique suggested by Brezzi, Fortin, and Marini\n[19]. We establish the discrete inf-sup conditions, and consequently present the a priori error analysis for them. The main ingredient for the analysis are two special interpolation operators, which can be constructed using a crucial \n \n \n \n \ud835\udc6f<\/m:mi>\n \u2062<\/m:mo>\n \n (<\/m:mo>\n div<\/m:mo>\n )<\/m:mo>\n <\/m:mrow>\n <\/m:mrow>\n <\/m:math>\n ${\\boldsymbol{H}(\\operatorname{div})}$<\/jats:tex-math>\n <\/jats:alternatives>\n <\/jats:inline-formula> bubble function space of polynomials on each element. The feature of these methods is the low number of global degrees of freedom in the lowest order case. We present some numerical results to demonstrate the theoretical estimates.<\/jats:p>","DOI":"10.1515\/cmam-2016-0035","type":"journal-article","created":{"date-parts":[[2016,11,10]],"date-time":"2016-11-10T10:01:17Z","timestamp":1478772077000},"page":"17-31","source":"Crossref","is-referenced-by-count":17,"title":["Stabilized Mixed Finite Element Methods for Linear Elasticity on Simplicial Grids in\n\u211dn<\/sup>"],"prefix":"10.1515","volume":"17","author":[{"given":"Long","family":"Chen","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA"}]},{"given":"Jun","family":"Hu","sequence":"additional","affiliation":[{"name":"LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China"}]},{"given":"Xuehai","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2016,11,10]]},"reference":[{"key":"2023033115185140896_j_cmam-2016-0035_ref_001_w2aab3b7e3597b1b6b1ab2b1b1Aa","doi-asserted-by":"crossref","unstructured":"Adams S. and Cockburn B.,\nA mixed finite element method for elasticity in three dimensions,\nJ. Sci. Comput. 25 (2005), 515\u2013521.","DOI":"10.1007\/s10915-004-4807-3"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_002_w2aab3b7e3597b1b6b1ab2b1b2Aa","doi-asserted-by":"crossref","unstructured":"Amara M. and Thomas J. M.,\nEquilibrium finite elements for the linear elastic problem,\nNumer. Math. 33 (1979), 367\u2013383.","DOI":"10.1007\/BF01399320"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_003_w2aab3b7e3597b1b6b1ab2b1b3Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N. and Awanou G.,\nRectangular mixed finite elements for elasticity,\nMath. Models Methods Appl. Sci. 15 (2005), 1417\u20131429.","DOI":"10.1142\/S0218202505000741"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_004_w2aab3b7e3597b1b6b1ab2b1b4Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N., Awanou G. and Winther R.,\nFinite elements for symmetric tensors in three dimensions,\nMath. Comp. 77 (2008), 1229\u20131251.","DOI":"10.1090\/S0025-5718-08-02071-1"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_005_w2aab3b7e3597b1b6b1ab2b1b5Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N., Awanou G. and Winther R.,\nNonconforming tetrahedral mixed finite elements for elasticity,\nMath. Models Methods Appl. Sci. 24 (2014), 783\u2013796.","DOI":"10.1142\/S021820251350067X"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_006_w2aab3b7e3597b1b6b1ab2b1b6Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N., Brezzi F. and Douglas, Jr. J.,\nPEERS: A new mixed finite element for plane elasticity,\nJapan J. Appl. Math. 1 (1984), 347\u2013367.","DOI":"10.1007\/BF03167064"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_007_w2aab3b7e3597b1b6b1ab2b1b7Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N., Douglas, Jr. J. and Gupta C. P.,\nA family of higher order mixed finite element methods for plane elasticity,\nNumer. Math. 45 (1984), 1\u201322.","DOI":"10.1007\/BF01379659"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_008_w2aab3b7e3597b1b6b1ab2b1b8Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N., Falk R. S. and Winther R.,\nMixed finite element methods for linear elasticity with weakly imposed symmetry,\nMath. Comp. 76 (2007), 1699\u20131723.","DOI":"10.1090\/S0025-5718-07-01998-9"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_009_w2aab3b7e3597b1b6b1ab2b1b9Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N. and Lee J. J.,\nMixed methods for elastodynamics with weak symmetry,\nSIAM J. Numer. Anal. 52 (2014), 2743\u20132769.","DOI":"10.1137\/13095032X"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_010_w2aab3b7e3597b1b6b1ab2b1c10Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N. and Winther R.,\nMixed finite elements for elasticity,\nNumer. Math. 92 (2002), 401\u2013419.","DOI":"10.1007\/s002110100348"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_011_w2aab3b7e3597b1b6b1ab2b1c11Aa","doi-asserted-by":"crossref","unstructured":"Arnold D. N. and Winther R.,\nNonconforming mixed elements for elasticity,\nMath. Models Methods Appl. Sci. 13 (2003), 295\u2013307.","DOI":"10.1142\/S0218202503002507"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_012_w2aab3b7e3597b1b6b1ab2b1c12Aa","doi-asserted-by":"crossref","unstructured":"Awanou G.,\nTwo remarks on rectangular mixed finite elements for elasticity,\nJ. Sci. Comput. 50 (2012), 91\u2013102.","DOI":"10.1007\/s10915-011-9474-6"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_013_w2aab3b7e3597b1b6b1ab2b1c13Aa","doi-asserted-by":"crossref","unstructured":"Boffi D.,\nStability of higher order triangular Hood\u2013Taylor methods for the stationary Stokes equations,\nMath. Models Methods Appl. Sci. 4 (1994), 223\u2013235.","DOI":"10.1142\/S0218202594000133"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_014_w2aab3b7e3597b1b6b1ab2b1c14Aa","doi-asserted-by":"crossref","unstructured":"Boffi D.,\nThree-dimensional finite element methods for the Stokes problem,\nSIAM J. Numer. Anal. 34 (1997), 664\u2013670.","DOI":"10.1137\/S0036142994270193"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_015_w2aab3b7e3597b1b6b1ab2b1c15Aa","doi-asserted-by":"crossref","unstructured":"Boffi D., Brezzi F. and Fortin M.,\nReduced symmetry elements in linear elasticity,\nCommun. Pure Appl. Anal. 8 (2009), 95\u2013121.","DOI":"10.3934\/cpaa.2009.8.95"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_016_w2aab3b7e3597b1b6b1ab2b1c16Aa","doi-asserted-by":"crossref","unstructured":"Boffi D., Brezzi F. and Fortin M.,\nMixed Finite Element Methods and Applications,\nSpringer Ser. Comput. Math. 44,\nSpringer, Berlin, 2013.","DOI":"10.1007\/978-3-642-36519-5"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_017_w2aab3b7e3597b1b6b1ab2b1c17Aa","doi-asserted-by":"crossref","unstructured":"Brenner S. C. and Scott L. R.,\nThe Mathematical Theory of Finite Element Methods, 3rd ed.,\nTexts Appl. Math. 15,\nSpringer, New York, 2008.","DOI":"10.1007\/978-0-387-75934-0"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_018_w2aab3b7e3597b1b6b1ab2b1c18Aa","doi-asserted-by":"crossref","unstructured":"Brezzi F.,\nOn the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers,\nRev. Franc. Automat. Inform. Rech. Operat. S\u00e9r. Rouge 8 (1974), 129\u2013151.","DOI":"10.1051\/m2an\/197408R201291"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_019_w2aab3b7e3597b1b6b1ab2b1c19Aa","doi-asserted-by":"crossref","unstructured":"Brezzi F., Fortin M. and Marini L. D.,\nMixed finite element methods with continuous stresses,\nMath. Models Methods Appl. Sci. 3 (1993), 275\u2013287.","DOI":"10.1142\/S0218202593000151"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_020_w2aab3b7e3597b1b6b1ab2b1c20Aa","unstructured":"Bustinza R.,\nA note on the local discontinuous Galerkin method forlinear problems in elasticity,\nSci. Ser. A Math. Sci. (N.S.) 13 (2006), 72\u201383."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_021_w2aab3b7e3597b1b6b1ab2b1c21Aa","doi-asserted-by":"crossref","unstructured":"Cai Z. and Ye X.,\nA mixed nonconforming finite element for linear elasticity,\nNumer. Methods Partial Differential Equations 21 (2005), 1043\u20131051.","DOI":"10.1002\/num.20075"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_022_w2aab3b7e3597b1b6b1ab2b1c22Aa","doi-asserted-by":"crossref","unstructured":"Chen G. and Xie X.,\nA robust weak Galerkin finite element method for linear elasticity with strong symmetric stresses,\nComput. Methods Appl. Math. 16 (2016), 389\u2013408.","DOI":"10.1515\/cmam-2016-0012"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_023_w2aab3b7e3597b1b6b1ab2b1c23Aa","doi-asserted-by":"crossref","unstructured":"Chen S.-C. and Wang Y.-N.,\nConforming rectangular mixed finite elements for elasticity,\nJ. Sci. Comput. 47 (2011), 93\u2013108.","DOI":"10.1007\/s10915-010-9422-x"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_024_w2aab3b7e3597b1b6b1ab2b1c24Aa","doi-asserted-by":"crossref","unstructured":"Chen Y., Huang J., Huang X. and Xu Y.,\nOn the local discontinuous Galerkin method for linear elasticity,\nMath. Probl. Eng. 2010 (2010), Article ID 759547.","DOI":"10.1155\/2010\/759547"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_025_w2aab3b7e3597b1b6b1ab2b1c25Aa","doi-asserted-by":"crossref","unstructured":"Ciarlet P. G.,\nThe Finite Element Method for Elliptic Problems,\nStud. Math. Appl. 4,\nNorth-Holland, Amsterdam, 1978.","DOI":"10.1115\/1.3424474"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_026_w2aab3b7e3597b1b6b1ab2b1c26Aa","doi-asserted-by":"crossref","unstructured":"Cockburn B., Gopalakrishnan J. and Guzm\u00e1n J.,\nA new elasticity element made for enforcing weak stress symmetry,\nMath. Comp. 79 (2010), 1331\u20131349.","DOI":"10.1090\/S0025-5718-10-02343-4"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_027_w2aab3b7e3597b1b6b1ab2b1c27Aa","doi-asserted-by":"crossref","unstructured":"Cockburn B., Sch\u00f6tzau D. and Wang J.,\nDiscontinuous Galerkin methods for incompressible elastic materials,\nComput. Methods Appl. Mech. Engrg. 195 (2006), 3184\u20133204.","DOI":"10.1016\/j.cma.2005.07.003"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_028_w2aab3b7e3597b1b6b1ab2b1c28Aa","doi-asserted-by":"crossref","unstructured":"Cockburn B. and Shi K.,\nSuperconvergent HDG methods for linear elasticity with weakly symmetric stresses,\nIMA J. Numer. Anal. 33 (2013), 747\u2013770.","DOI":"10.1093\/imanum\/drs020"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_029_w2aab3b7e3597b1b6b1ab2b1c29Aa","doi-asserted-by":"crossref","unstructured":"Di Pietro D. A. and Ern A.,\nA hybrid high-order locking-free method for linear elasticity on general meshes,\nComput. Methods Appl. Mech. Engrg. 283 (2015), 1\u201321.","DOI":"10.1016\/j.cma.2014.09.009"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_030_w2aab3b7e3597b1b6b1ab2b1c30Aa","unstructured":"Fraeijs de Veubeke B.,\nDisplacement and equilibrium models in the finite element method,\nStress Analysis,\nJohn Wiley & Sons, New York (1965), 145\u2013197."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_031_w2aab3b7e3597b1b6b1ab2b1c31Aa","unstructured":"Gong S., Wu S. and Xu J.,\nMixed finite elements of any order in any dimension for linear elasticity with strongly symmetric stress tensor,\npreprint 2015, http:\/\/arxiv.org\/abs\/1507.01752."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_032_w2aab3b7e3597b1b6b1ab2b1c32Aa","doi-asserted-by":"crossref","unstructured":"Gopalakrishnan J. and Guzm\u00e1n J.,\nSymmetric nonconforming mixed finite elements for linear elasticity,\nSIAM J. Numer. Anal. 49 (2011), 1504\u20131520.","DOI":"10.1137\/10080018X"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_033_w2aab3b7e3597b1b6b1ab2b1c33Aa","doi-asserted-by":"crossref","unstructured":"Gopalakrishnan J. and Guzm\u00e1n J.,\nA second elasticity element using the matrix bubble,\nIMA J. Numer. Anal. 32 (2012), 352\u2013372.","DOI":"10.1093\/imanum\/drq047"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_034_w2aab3b7e3597b1b6b1ab2b1c34Aa","doi-asserted-by":"crossref","unstructured":"Guzm\u00e1n J.,\nA unified analysis of several mixed methods for elasticity with weak stress symmetry,\nJ. Sci. Comput. 44 (2010), 156\u2013169.","DOI":"10.1007\/s10915-010-9373-2"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_035_w2aab3b7e3597b1b6b1ab2b1c35Aa","doi-asserted-by":"crossref","unstructured":"Harder C., Madureira A. L. and Valentin F.,\nA hybrid-mixed method for elasticity,\nESAIM Math. Model. Numer. Anal. 50 (2016), 311\u2013336.","DOI":"10.1051\/m2an\/2015046"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_036_w2aab3b7e3597b1b6b1ab2b1c36Aa","doi-asserted-by":"crossref","unstructured":"Hu J.,\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), 1438\u20131463.","DOI":"10.1137\/130945272"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_037_w2aab3b7e3597b1b6b1ab2b1c37Aa","doi-asserted-by":"crossref","unstructured":"Hu J.,\nFinite element approximations of symmetric tensors on simplicial grids in \u211dn${\\mathbb{R}^{n}}$: The higher order case,\nJ. Comput. Math. 33 (2015), 283\u2013296.","DOI":"10.4208\/jcm.1412-m2014-0071"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_038_w2aab3b7e3597b1b6b1ab2b1c38Aa","doi-asserted-by":"crossref","unstructured":"Hu J., Man H. and Zhang S.,\nA simple conforming mixed finite element for linear elasticity on rectangular grids in any space dimension,\nJ. Sci. Comput. 58 (2014), 367\u2013379.","DOI":"10.1007\/s10915-013-9736-6"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_039_w2aab3b7e3597b1b6b1ab2b1c39Aa","doi-asserted-by":"crossref","unstructured":"Hu J. and Shi Z.-C.,\nLower order rectangular nonconforming mixed finite elements for plane elasticity,\nSIAM J. Numer. Anal. 46 (2007), 88\u2013102.","DOI":"10.1137\/060669681"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_040_w2aab3b7e3597b1b6b1ab2b1c40Aa","unstructured":"Hu J. and Zhang S.,\nA family of conforming mixed finite elements for linear elasticity on triangular grids,\npreprint 2015, http:\/\/arxiv.org\/abs\/1406.7457."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_041_w2aab3b7e3597b1b6b1ab2b1c41Aa","doi-asserted-by":"crossref","unstructured":"Hu J. and Zhang S.,\nA family of symmetric mixed finite elements for linear elasticity on tetrahedral grids,\nSci. China Math. 58 (2015), 297\u2013307.","DOI":"10.1007\/s11425-014-4953-5"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_042_w2aab3b7e3597b1b6b1ab2b1c42Aa","doi-asserted-by":"crossref","unstructured":"Hu J. and Zhang S.,\nFinite element approximations of symmetric tensors on simplicial grids in \u211dn$\\mathbb{R}^{n}$: The lower order case,\nMath. Models Methods Appl. Sci. 26 (2016), 1649\u20131669.","DOI":"10.1142\/S0218202516500408"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_043_w2aab3b7e3597b1b6b1ab2b1c43Aa","unstructured":"Huang J. and Huang X.,\nThe hp-version error analysis of a mixed DG method for linear elasticity,\npreprint 2016, http:\/\/arxiv.org\/abs\/1608.04060."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_044_w2aab3b7e3597b1b6b1ab2b1c44Aa","doi-asserted-by":"crossref","unstructured":"Huang X.,\nA reduced local discontinuous Galerkin method for nearly incompressible linear elasticity,\nMath. Probl. Eng. 2013 (2013), Article ID 546408.","DOI":"10.1155\/2013\/546408"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_045_w2aab3b7e3597b1b6b1ab2b1c45Aa","doi-asserted-by":"crossref","unstructured":"Huang X. and Huang J.,\nThe compact discontinuous Galerkin method for nearly incompressible linear elasticity,\nJ. Sci. Comput. 56 (2013), 291\u2013318.","DOI":"10.1007\/s10915-012-9676-6"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_046_w2aab3b7e3597b1b6b1ab2b1c46Aa","doi-asserted-by":"crossref","unstructured":"Johnson C. and Mercier B.,\nSome equilibrium finite element methods for two-dimensional elasticity problems,\nNumer. Math. 30 (1978), 103\u2013116.","DOI":"10.1007\/BF01403910"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_047_w2aab3b7e3597b1b6b1ab2b1c47Aa","doi-asserted-by":"crossref","unstructured":"Man H.-Y., Hu J. and Shi Z.-C.,\nLower order rectangular nonconforming mixed finite element for the three-dimensional elasticity problem,\nMath. Models Methods Appl. Sci. 19 (2009), 51\u201365.","DOI":"10.1142\/S0218202509003358"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_048_w2aab3b7e3597b1b6b1ab2b1c48Aa","doi-asserted-by":"crossref","unstructured":"Morley M. E.,\nA family of mixed finite elements for linear elasticity,\nNumer. Math. 55 (1989), 633\u2013666.","DOI":"10.1007\/BF01389334"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_049_w2aab3b7e3597b1b6b1ab2b1c49Aa","doi-asserted-by":"crossref","unstructured":"Qiu W. and Demkowicz L.,\nMixed hp-finite element method for linear elasticity with weakly imposed symmetry,\nComput. Methods Appl. Mech. Engrg. 198 (2009), 3682\u20133701.","DOI":"10.1016\/j.cma.2009.07.010"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_050_w2aab3b7e3597b1b6b1ab2b1c50Aa","doi-asserted-by":"crossref","unstructured":"Qiu W. and Demkowicz L.,\nMixed hp-finite element method for linear elasticity with weakly imposed symmetry: Stability analysis,\nSIAM J. Numer. Anal. 49 (2011), 619\u2013641.","DOI":"10.1137\/100797539"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_051_w2aab3b7e3597b1b6b1ab2b1c51Aa","unstructured":"Qiu W., Shen J. and Shi K.,\nAn HDG method for linear elasticity with strong symmetric stresses,\npreprint 2013, http:\/\/arxiv.org\/abs\/1312.1407."},{"key":"2023033115185140896_j_cmam-2016-0035_ref_052_w2aab3b7e3597b1b6b1ab2b1c52Aa","doi-asserted-by":"crossref","unstructured":"Scott L. R. and Zhang S.,\nFinite element interpolation of nonsmooth functions satisfying boundary conditions,\nMath. Comp. 54 (1990), 483\u2013493.","DOI":"10.1090\/S0025-5718-1990-1011446-7"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_053_w2aab3b7e3597b1b6b1ab2b1c53Aa","doi-asserted-by":"crossref","unstructured":"Stenberg R.,\nA family of mixed finite elements for the elasticity problem,\nNumer. Math. 53 (1988), 513\u2013538.","DOI":"10.1007\/BF01397550"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_054_w2aab3b7e3597b1b6b1ab2b1c54Aa","doi-asserted-by":"crossref","unstructured":"Taylor C. and Hood P.,\nA numerical solution of the Navier\u2013Stokes equations using the finite element technique,\nComput. & Fluids 1 (1973), 73\u2013100.","DOI":"10.1016\/0045-7930(73)90027-3"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_055_w2aab3b7e3597b1b6b1ab2b1c55Aa","doi-asserted-by":"crossref","unstructured":"Wang C., Wang J., Wang R. and Zhang R.,\nA locking-free weak Galerkin finite element method for elasticity problems in the primal formulation,\nJ. Comput. Appl. Math. 307 (2016), 346\u2013366.","DOI":"10.1016\/j.cam.2015.12.015"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_056_w2aab3b7e3597b1b6b1ab2b1c56Aa","doi-asserted-by":"crossref","unstructured":"Watwood, Jr. V. B. and Hartz B. J.,\nAn equilibrium stress field model for finite element solutions of two-dimensional elastostatic problems,\nInt. J. Solids Struct. 4 (1968), 857\u2013873.","DOI":"10.1016\/0020-7683(68)90083-8"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_057_w2aab3b7e3597b1b6b1ab2b1c57Aa","doi-asserted-by":"crossref","unstructured":"Xie X. and Xu J.,\nNew mixed finite elements for plane elasticity and Stokes equations,\nSci. China Math. 54 (2011), 1499\u20131519.","DOI":"10.1007\/s11425-011-4171-3"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_058_w2aab3b7e3597b1b6b1ab2b1c58Aa","doi-asserted-by":"crossref","unstructured":"Yi S.-Y.,\nNonconforming mixed finite element methods for linear elasticity using rectangular elements in two and three dimensions,\nCalcolo 42 (2005), 115\u2013133.","DOI":"10.1007\/s10092-005-0101-5"},{"key":"2023033115185140896_j_cmam-2016-0035_ref_059_w2aab3b7e3597b1b6b1ab2b1c59Aa","doi-asserted-by":"crossref","unstructured":"Yi S.-Y.,\nA new nonconforming mixed finite element method for linear elasticity,\nMath. Models Methods Appl. Sci. 16 (2006), 979\u2013999.","DOI":"10.1142\/S0218202506001431"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/17\/1\/article-p17.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0035\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0035\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T22:02:47Z","timestamp":1680300167000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2016-0035\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,10]]},"references-count":59,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2016,9,18]]},"published-print":{"date-parts":[[2017,1,1]]}},"alternative-id":["10.1515\/cmam-2016-0035"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2016-0035","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2016,11,10]]}}}