Sun, Bohua On Chien’s question to the Hu-Washizu three-field functional and variational principle. (English) Zbl 1496.35381 AMM, Appl. Math. Mech., Engl. Ed. 43, No. 4, 537-546 (2022). MSC: 35Q74 35A15 37D35 49S05 74B05 74A15 74D10 PDF BibTeX XML Cite \textit{B. Sun}, AMM, Appl. Math. Mech., Engl. Ed. 43, No. 4, 537--546 (2022; Zbl 1496.35381) Full Text: DOI OpenURL
Dhas, Bensingh; Kumar, N. Jamun; Roy, Debasish; Reddy, J. N. A mixed variational principle in nonlinear elasticity using Cartan’s moving frames and implementation with finite element exterior calculus. (English) Zbl 1507.74072 Comput. Methods Appl. Mech. Eng. 393, Article ID 114756, 28 p. (2022). MSC: 74B20 49K05 49S05 74S05 65N30 PDF BibTeX XML Cite \textit{B. Dhas} et al., Comput. Methods Appl. Mech. Eng. 393, Article ID 114756, 28 p. (2022; Zbl 1507.74072) Full Text: DOI arXiv OpenURL
Hu, Jun; Ma, Rui; Zhang, Min A family of mixed finite elements for the biharmonic equations on triangular and tetrahedral grids. (English) Zbl 1491.65141 Sci. China, Math. 64, No. 12, 2793-2816 (2021). MSC: 65N30 65N12 31A30 74S05 PDF BibTeX XML Cite \textit{J. Hu} et al., Sci. China, Math. 64, No. 12, 2793--2816 (2021; Zbl 1491.65141) Full Text: DOI arXiv OpenURL
Song, Shicang; Lu, Lijuan A nonconforming scheme with piecewise quasi three degree polynomial space to solve biharmonic problem. (English) Zbl 1475.65202 J. Appl. Math. Comput. 66, No. 1-2, 581-597 (2021). MSC: 65N30 PDF BibTeX XML Cite \textit{S. Song} and \textit{L. Lu}, J. Appl. Math. Comput. 66, No. 1--2, 581--597 (2021; Zbl 1475.65202) Full Text: DOI OpenURL
Liu, Zhixin; Song, Shicang An isoparametric mixed finite element method for approximating a class of fourth-order elliptic problem. (English) Zbl 07362375 Comput. Math. Appl. 96, 77-94 (2021). MSC: 65N30 65N15 35J40 74S05 35J25 PDF BibTeX XML Cite \textit{Z. Liu} and \textit{S. Song}, Comput. Math. Appl. 96, 77--94 (2021; Zbl 07362375) Full Text: DOI OpenURL
Brenner, Susanne C. Finite element methods for elliptic distributed optimal control problems with pointwise state constraints (survey). (English) Zbl 1440.49037 Acu, Bahar (ed.) et al., Advances in mathematical sciences. AWM research symposium, Houston, TX, USA, April 6–7, 2019. Cham: Springer. Assoc. Women Math. Ser. 21, 3-16 (2020). MSC: 49M25 65K15 65N30 PDF BibTeX XML Cite \textit{S. C. Brenner}, Assoc. Women Math. Ser. 21, 3--16 (2020; Zbl 1440.49037) Full Text: DOI arXiv OpenURL
Hu, Jun; Tian, Shudan; Zhang, Shangyou A family of 3D \(H^2\)-nonconforming tetrahedral finite elements for the biharmonic equation. (English) Zbl 1446.65171 Sci. China, Math. 63, No. 8, 1505-1522 (2020). MSC: 65N30 65N15 31A30 PDF BibTeX XML Cite \textit{J. Hu} et al., Sci. China, Math. 63, No. 8, 1505--1522 (2020; Zbl 1446.65171) Full Text: DOI arXiv OpenURL
González, José A.; Park, K. C. Accelerating the convergence of AFETI partitioned analysis of heterogeneous structural dynamical systems. (English) Zbl 1441.65053 Comput. Methods Appl. Mech. Eng. 360, Article ID 112726, 26 p. (2020). MSC: 65K10 PDF BibTeX XML Cite \textit{J. A. González} and \textit{K. C. Park}, Comput. Methods Appl. Mech. Eng. 360, Article ID 112726, 26 p. (2020; Zbl 1441.65053) Full Text: DOI OpenURL
Wu, Shuonan; Xu, Jinchao Nonconforming finite element spaces for \(2m\)th order partial differential equations on \(\mathbb {R}^n\) simplicial grids when \(m=n+1\). (English) Zbl 1407.65304 Math. Comput. 88, No. 316, 531-551 (2019). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N12 65N15 35B25 35J30 PDF BibTeX XML Cite \textit{S. Wu} and \textit{J. Xu}, Math. Comput. 88, No. 316, 531--551 (2019; Zbl 1407.65304) Full Text: DOI arXiv OpenURL
Brenner, Susanne C.; Sung, Li-yeng A new convergence analysis of finite element methods for elliptic distributed optimal control problems with pointwise state constraints. (English) Zbl 1370.49006 SIAM J. Control Optim. 55, No. 4, 2289-2304 (2017). MSC: 49J40 49J20 65K15 65N30 49J45 PDF BibTeX XML Cite \textit{S. C. Brenner} and \textit{L.-y. Sung}, SIAM J. Control Optim. 55, No. 4, 2289--2304 (2017; Zbl 1370.49006) Full Text: DOI OpenURL
Zhao, Jikun; Chen, Shaochun; Zhang, Bei The nonconforming virtual element method for plate bending problems. (English) Zbl 1396.74098 Math. Models Methods Appl. Sci. 26, No. 9, 1671-1687 (2016). MSC: 74S05 65N30 65N12 74K20 PDF BibTeX XML Cite \textit{J. Zhao} et al., Math. Models Methods Appl. Sci. 26, No. 9, 1671--1687 (2016; Zbl 1396.74098) Full Text: DOI OpenURL
Shi, Dongyang; Pei, Lifang Double set parameter finite element method for two-sided displacement obstacle problem of clamped plate. (English) Zbl 1335.74055 J. Math. Anal. Appl. 436, No. 1, 203-216 (2016). MSC: 74S05 65N30 49J40 65K15 65N15 74K20 PDF BibTeX XML Cite \textit{D. Shi} and \textit{L. Pei}, J. Math. Anal. Appl. 436, No. 1, 203--216 (2016; Zbl 1335.74055) Full Text: DOI OpenURL
Shi, Dongyang; Pei, Lifang Nonconforming double set parameter finite element methods for a fourth order variational inequality with two-sided displacement obstacle. (English) Zbl 1333.65133 J. Inequal. Appl. 2015, Paper No. 246, 17 p. (2015). MSC: 65N30 65N15 PDF BibTeX XML Cite \textit{D. Shi} and \textit{L. Pei}, J. Inequal. Appl. 2015, Paper No. 246, 17 p. (2015; Zbl 1333.65133) Full Text: DOI OpenURL
Brenner, Susanne C. Forty years of the Crouzeix-Raviart element. (English) Zbl 1310.65142 Numer. Methods Partial Differ. Equations 31, No. 2, 367-396 (2015). MSC: 65N30 65-03 01A60 01A61 PDF BibTeX XML Cite \textit{S. C. Brenner}, Numer. Methods Partial Differ. Equations 31, No. 2, 367--396 (2015; Zbl 1310.65142) Full Text: DOI OpenURL
Sun, Ming; Song, Shicang; Liu, Zeyi A nonconforming scheme with high accuracy for the plate bending problem. (English) Zbl 1367.74049 Comput. Math. Appl. 68, No. 10, 1083-1092 (2014). MSC: 74S05 74K20 65N30 65N12 PDF BibTeX XML Cite \textit{M. Sun} et al., Comput. Math. Appl. 68, No. 10, 1083--1092 (2014; Zbl 1367.74049) Full Text: DOI OpenURL
Chen, Hong-Ru; Chen, Shao-Chun; Qiao, Zhong-Hua \(C^0\)-nonconforming triangular prism elements for the three-dimensional fourth-order elliptic problem. (English) Zbl 1269.65122 J. Sci. Comput. 55, No. 3, 645-658 (2013). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 65N12 35J40 PDF BibTeX XML Cite \textit{H.-R. Chen} et al., J. Sci. Comput. 55, No. 3, 645--658 (2013; Zbl 1269.65122) Full Text: DOI OpenURL
Park, Chunjae; Sheen, Dongwoo A quadrilateral Morley element for biharmonic equations. (English) Zbl 1316.74063 Numer. Math. 124, No. 2, 395-413 (2013). MSC: 74S05 65N30 PDF BibTeX XML Cite \textit{C. Park} and \textit{D. Sheen}, Numer. Math. 124, No. 2, 395--413 (2013; Zbl 1316.74063) Full Text: DOI OpenURL
Chen, Hongru; Chen, Shaochun; Qiao, Zhonghua \(C^{0}\)-nonconforming tetrahedral and cuboid elements for the three-dimensional fourth-order elliptic problem. (English) Zbl 1276.65078 Numer. Math. 124, No. 1, 99-119 (2013). Reviewer: Adrian Carabineanu (Bucureşti) MSC: 65N30 65N15 65N12 35J30 PDF BibTeX XML Cite \textit{H. Chen} et al., Numer. Math. 124, No. 1, 99--119 (2013; Zbl 1276.65078) Full Text: DOI OpenURL
Wang, Ming; Xu, Jinchao Minimal finite element spaces for \(2m\)-th-order partial differential equations in \(\mathbb{R}^n\). (English) Zbl 1264.65199 Math. Comput. 82, No. 281, 25-43 (2013). Reviewer: Abdallah Bradji (Annaba) MSC: 65N30 65N15 35J05 35J40 65N12 PDF BibTeX XML Cite \textit{M. Wang} and \textit{J. Xu}, Math. Comput. 82, No. 281, 25--43 (2013; Zbl 1264.65199) Full Text: DOI OpenURL
Wang, Ming; Zu, PengHe; Zhang, Shuo High accuracy nonconforming finite elements for fourth-order problems. (English) Zbl 1264.65200 Sci. China, Math. 55, No. 10, 2183-2192 (2012). Reviewer: Jiguang Sun (Dover) MSC: 65N30 35J40 65N12 PDF BibTeX XML Cite \textit{M. Wang} et al., Sci. China, Math. 55, No. 10, 2183--2192 (2012; Zbl 1264.65200) Full Text: DOI OpenURL
Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Yi Finite element methods for the displacement obstacle problem of clamped plates. (English) Zbl 1250.74023 Math. Comput. 81, No. 279, 1247-1262 (2012). Reviewer: Jan Lovíšek (Bratislava) MSC: 74S05 74M15 74K20 65N30 65N12 49J40 PDF BibTeX XML Cite \textit{S. C. Brenner} et al., Math. Comput. 81, No. 279, 1247--1262 (2012; Zbl 1250.74023) Full Text: DOI OpenURL
Huang, Jianguo; Huang, Xuehai; Han, Weimin A new discontinuous Galerkin method for Kirchhoff plates. (English) Zbl 1231.74416 Comput. Methods Appl. Mech. Eng. 199, No. 23-24, 1446-1454 (2010). MSC: 74S05 74K20 PDF BibTeX XML Cite \textit{J. Huang} et al., Comput. Methods Appl. Mech. Eng. 199, No. 23--24, 1446--1454 (2010; Zbl 1231.74416) Full Text: DOI OpenURL
Jabareen, M.; Rubin, M. B. Failures of the three-dimensional patch test for large elastic deformations. (English) Zbl 1323.74087 Int. J. Numer. Methods Biomed. Eng. 26, No. 12, 1618-1624 (2010). MSC: 74S05 74B20 PDF BibTeX XML Cite \textit{M. Jabareen} and \textit{M. B. Rubin}, Int. J. Numer. Methods Biomed. Eng. 26, No. 12, 1618--1624 (2010; Zbl 1323.74087) Full Text: DOI OpenURL
Bourgeois, Laurent; Dardé, Jérémi About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains. (English) Zbl 1206.35252 Appl. Anal. 89, No. 11, 1745-1768 (2010). MSC: 35R25 35A15 35A27 35N25 65N30 35B35 PDF BibTeX XML Cite \textit{L. Bourgeois} and \textit{J. Dardé}, Appl. Anal. 89, No. 11, 1745--1768 (2010; Zbl 1206.35252) Full Text: DOI OpenURL
Rajendran, S.; Ooi, E. T.; Yeo, J. H. Mesh-distortion immunity assessment of QUAD8 elements by strong-form patch tests. (English) Zbl 1107.74046 Commun. Numer. Methods Eng. 23, No. 2, 157-168 (2007). MSC: 74S05 74B05 PDF BibTeX XML Cite \textit{S. Rajendran} et al., Commun. Numer. Methods Eng. 23, No. 2, 157--168 (2007; Zbl 1107.74046) Full Text: DOI OpenURL
Gal, Erez; Levy, Robert Geometrically nonlinear analysis of shell structures using a flat triangular shell finite element. (English) Zbl 1104.74058 Arch. Comput. Methods Eng. 13, No. 3, 331-388 (2006). MSC: 74S05 74K25 74-02 PDF BibTeX XML Cite \textit{E. Gal} and \textit{R. Levy}, Arch. Comput. Methods Eng. 13, No. 3, 331--388 (2006; Zbl 1104.74058) Full Text: DOI OpenURL
Paraskevopoulos, Elias; Talaslidis, Demosthenes Reduction of excessive energy in the four-noded membrane quadrilateral element. I: Linear theory – compressible materials. (English) Zbl 1090.74058 Comput. Methods Appl. Mech. Eng. 194, No. 36-38, 3771-3796 (2005). MSC: 74S05 74K15 PDF BibTeX XML Cite \textit{E. Paraskevopoulos} and \textit{D. Talaslidis}, Comput. Methods Appl. Mech. Eng. 194, No. 36--38, 3771--3796 (2005; Zbl 1090.74058) Full Text: DOI OpenURL
Park, K. C.; Felippa, C. A.; Rebel, G. A simple algorithm for localized construction of non-matching structural interfaces. (English) Zbl 1169.74653 Int. J. Numer. Methods Eng. 53, No. 9, 2117-2142 (2002). MSC: 74S30 74K99 PDF BibTeX XML Cite \textit{K. C. Park} et al., Int. J. Numer. Methods Eng. 53, No. 9, 2117--2142 (2002; Zbl 1169.74653) Full Text: DOI OpenURL
Mallikarjuna Rao, K.; Shrinivasa, U. A set of pathological test to validate new finite elements. (English) Zbl 1023.74047 Sādhanā 26, No. 6, 549-590 (2001). MSC: 74S05 65N30 PDF BibTeX XML Cite \textit{K. Mallikarjuna Rao} and \textit{U. Shrinivasa}, Sādhanā 26, No. 6, 549--590 (2001; Zbl 1023.74047) Full Text: DOI OpenURL
Felippa, C. A. Recent developments in parametrized variational principles for mechanics. (English) Zbl 0866.73081 Comput. Mech. 18, No. 3, 159-174 (1996). MSC: 74S30 74P10 74B99 70H30 49S05 PDF BibTeX XML Cite \textit{C. A. Felippa}, Comput. Mech. 18, No. 3, 159--174 (1996; Zbl 0866.73081) Full Text: DOI OpenURL
Brenner, Susanne C. Two-level additive Schwarz preconditioners for plate elements. (English) Zbl 0968.74598 Wuhan Univ. J. Nat. Sci. 1, No. 3-4, 658-667 (1996). MSC: 74S05 74K20 PDF BibTeX XML Cite \textit{S. C. Brenner}, Wuhan Univ. J. Nat. Sci. 1, No. 3--4, 658--667 (1996; Zbl 0968.74598) Full Text: DOI OpenURL
Auricchio, F.; Taylor, R. L. A shear deformable plate element with an exact thin limit. (English) Zbl 0849.73063 Comput. Methods Appl. Mech. Eng. 118, No. 3-4, 393-412 (1994). MSC: 74S05 74K20 PDF BibTeX XML Cite \textit{F. Auricchio} and \textit{R. L. Taylor}, Comput. Methods Appl. Mech. Eng. 118, No. 3--4, 393--412 (1994; Zbl 0849.73063) Full Text: DOI OpenURL
Yu, Zhongzhi Generalized biharmonic operator and its application to the bending of elastic thin plates. (English) Zbl 0796.73033 Appl. Math. Mech., Engl. Ed. 15, No. 2, 167-174 (1994). MSC: 74K20 31A30 PDF BibTeX XML Cite \textit{Z. Yu}, Appl. Math. Mech., Engl. Ed. 15, No. 2, 167--174 (1994; Zbl 0796.73033) Full Text: DOI OpenURL
Ainsworth, Mark; Oden, J. Tinsley A unified approach to a posteriori error estimation using element residual methods. (English) Zbl 0797.65080 Numer. Math. 65, No. 1, 23-50 (1993). Reviewer: E.Lanckau (Chemnitz) MSC: 65N15 65N30 35J25 PDF BibTeX XML Cite \textit{M. Ainsworth} and \textit{J. T. Oden}, Numer. Math. 65, No. 1, 23--50 (1993; Zbl 0797.65080) Full Text: DOI EuDML OpenURL
Trouvé, P. Sur la convergence des méthodes d’éléments finis nonconformes pour des problèmes linéaires de coques minces. (On the convergence of nonconforming finite element method for linear thin shell problems). (French) Zbl 0673.73060 Numer. Math. 57, No. 5, 481-524 (1990). Reviewer: P.Trouvé MSC: 74S05 74K15 65N30 PDF BibTeX XML Cite \textit{P. Trouvé}, Numer. Math. 57, No. 5, 481--524 (1990; Zbl 0673.73060) Full Text: DOI EuDML OpenURL
Balasundaram, S.; Bhattacharyya, P. K. A mixed finite-element method for fourth-order elliptic problems with variable coefficients. (English) Zbl 0647.65075 J. Comput. Appl. Math. 22, No. 1, 1-24 (1988). Reviewer: D.R.Westbrook MSC: 65N30 65N15 74S05 35J40 PDF BibTeX XML Cite \textit{S. Balasundaram} and \textit{P. K. Bhattacharyya}, J. Comput. Appl. Math. 22, No. 1, 1--24 (1988; Zbl 0647.65075) Full Text: DOI OpenURL
Rubinstein, R.; Punch, E. F.; Atluri, S. N. An analysis of, and remedies for, kinematic modes in hybrid-stress finite elements: selection of stable, invariant stress fields. (English) Zbl 0519.73070 Comput. Methods Appl. Mech. Eng. 38, 63-92 (1983). MSC: 74S05 74S99 PDF BibTeX XML Cite \textit{R. Rubinstein} et al., Comput. Methods Appl. Mech. Eng. 38, 63--92 (1983; Zbl 0519.73070) Full Text: DOI OpenURL
Carnoy, Eric G. Mixed finite elements based upon Marguerre theory for the study of geometrically nonlinear behavior of thin shells. (English) Zbl 0466.73099 Comput. Methods Appl. Mech. Eng. 29, 121-146 (1981). MSC: 74S05 74K15 49S05 PDF BibTeX XML Cite \textit{E. G. Carnoy}, Comput. Methods Appl. Mech. Eng. 29, 121--146 (1981; Zbl 0466.73099) Full Text: DOI OpenURL
Quarteroni, A. Primal hybrid finite element methods for 4th order elliptic equations. (English) Zbl 0435.65092 Calcolo 16, 21-59 (1979). MSC: 65N30 74K20 31A30 35J40 PDF BibTeX XML Cite \textit{A. Quarteroni}, Calcolo 16, 21--59 (1979; Zbl 0435.65092) Full Text: DOI OpenURL
Bufler, H. Generalized variational principles with relaxed continuity requirements for certain nonlinear problems, with an application to nonlinear elasticity. (English) Zbl 0424.73018 Comput. Methods Appl. Mech. Eng. 19, 235-255 (1979). MSC: 74B20 74S05 49S05 PDF BibTeX XML Cite \textit{H. Bufler}, Comput. Methods Appl. Mech. Eng. 19, 235--255 (1979; Zbl 0424.73018) Full Text: DOI OpenURL
Ruas de Barros, V. Some results on the curved plate bending problem solved with non- conforming finite elements. (English) Zbl 0497.73074 Calcolo 15, 101-120 (1978). MSC: 74S05 74K20 65N30 PDF BibTeX XML Cite \textit{V. Ruas de Barros}, Calcolo 15, 101--120 (1978; Zbl 0497.73074) Full Text: DOI OpenURL
Babuška, Ivo; Oden, J. T.; Lee, J. K. Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. (English) Zbl 0382.65056 Computer Methods Appl. Mech. Engin. 11, 175-206 (1977). MSC: 65N30 35J25 65N15 PDF BibTeX XML Cite \textit{I. Babuška} et al., Comput. Methods Appl. Mech. Eng. 11, 175--206 (1977; Zbl 0382.65056) Full Text: DOI OpenURL
Fraeijs de Veubeke, B. M.; Millard, A. Discretization of stress fields in the finite element method. (English) Zbl 0352.73061 J. Franklin Inst. 302, 389-412 (1976). MSC: 74S05 65N30 PDF BibTeX XML Cite \textit{B. M. Fraeijs de Veubeke} and \textit{A. Millard}, J. Franklin Inst. 302, 389--412 (1976; Zbl 0352.73061) Full Text: DOI Link OpenURL
Brezzi, F.; Marini, L. D. On the numerical solution of plate bending problems by hybrid methods. (English) Zbl 0322.73048 Rev. Franc. Automat. Inform. Rech. Operat. 9, Analyse numer. R-3, 50 p. (1975). MSC: 74S05 74K20 65Z05 65N99 PDF BibTeX XML Cite \textit{F. Brezzi} and \textit{L. D. Marini}, Rev. Franc. Automat. Inform. Rech. Operat., R 9, No. 3, 50 p. (1975; Zbl 0322.73048) Full Text: EuDML OpenURL
Lascaux, P.; Lesaint, P. Some nonconforming finite elements for the plate bending problem. (English) Zbl 0319.73042 Rev. Franc. Automat. Inform. Rech. Operat. 9, Analyse numer. R-1, 9-53 (1975). MSC: 74S05 74K20 PDF BibTeX XML Cite \textit{P. Lascaux} and \textit{P. Lesaint}, Rev. Franc. Automat. Inform. Rech. Operat., R 9, No. 1, 9--53 (1975; Zbl 0319.73042) Full Text: EuDML OpenURL
Brezzi, F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. (English) Zbl 0338.90047 Rev. Franc. Automat. Inform. Rech. Operat. 8, Analyse numer., R-2, 129-151 (1974). MSC: 90C30 49K35 PDF BibTeX XML Cite \textit{F. Brezzi}, Rev. Franc. Automat. Inform. Rech. Operat., R 8, No. 2, 129--151 (1974; Zbl 0338.90047) Full Text: EuDML OpenURL