[1] Reddy B, Simo J. Stability and convergence of a class of enhanced strain methods[J]. SIAM J. Numer. Anal., 1995, 32(6):1705-1728.[2] Braess D, Carstensen C, Reddy B. Uniform convergence and a posteriori error estimators for the enhanced strain finite element method[J]. Numer. Math., 2004, 96(3):461-479.[3] Houston P, Schotzau D, Wihler T. An hp-adaptive mixed discontinuous Galerkin FEM for nearly incompressible linear elasticity[J]. Comput. Methods Appl. Mech. Engrg., 2006, 195(25-28):3224-3246.[4] Hansbo P, Larson M. Discontinuous Galerkin methods for incompressible and nearly incompressible elasticity by Nitsche's method[J]. Comput. Methods Appl. Mech. Engrg., 2002, 191(17-18):1895-1908.[5] Hong Q, Kraus J, Xu J, Zikatanov L. A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations[J]. Numer. Math., 2016, 132(1):23-49.[6] Wu S, Gong S, Xu J. Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor[J]. Math. Models Methods in Appl. Sci., 2017, 27(14):2711-2743.[7] Gong S, Wu S, Xu J. New hybridized mixed methods for linear elasticity and optimal multilevel solvers[J]. Numer. Math., 2019, 141(2):569-604.[8] Wang F, Wu S, Xu J. A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry[J]. J. Sci. Comput., 2020, 83(1):1-17.[9] Hong Q, Hu J, Ma L, Xu J. An Extended Galerkin Analysis for Linear Elasticity with Strongly Symmetric Stress Tensor[J]. arXiv preprint arXiv:2002.11664, 2020.[10] Auricchio F, da Veiga L B, Lovadina C, Reali A. A stability study of some mixed finite elements for large deformation elasticity problems[J]. Comput. Methods Appl. Mech. Engrg., 2005, 194(9-11):1075-1092.[11] Wriggers P, Reese S. A note on enhanced strain methods for large deformations[J]. Comput. Methods Appl. Mech. Engrg., 1996, 135(3-4):201-209.[12] Lovadina C, Auricchio F. On the enhanced strain technique for elasticity problems[J]. Comput.& Structures, 2003, 81(8-11):777-787.[13] Pantuso D, Bathe K. On the stability of mixed finite elements in large strain analysis of incompressible solids[J]. Finite Elem. Anal. Des., 1997, 28(2):83-104.[14] Eyck A T, Celiker F, Lew A. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity:Analytical estimates[J]. Comput. Methods Appl. Mech. Engrg., 2008, 197(33-40):2989-3000.[15] Eyck A T, Celiker F, Lew A. Adaptive stabilization of discontinuous Galerkin methods for nonlinear elasticity:Motivation, formulation, and numerical examples[J]. Comput. Methods Appl. Mech. Engrg., 2008, 197(45-48):3605-3622.[16] A. Ten Eyck A, Lew A. An adaptive stabilization strategy for enhanced strain methods in nonlinear elasticity[J]. Internat. J. Numer. Methods Engrg., 2010, 81(11):1387-1416.[17] Auricchio F, da Veiga L B, Lovadina C, Reali A. The importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity:mixed FEMs versus NURBS-based approximations[J]. Comput. Methods Appl. Mech. Engrg., 2010, 199(5-8):314-323.[18] Hughes T, Cottrell J, Bazilevs Y. Isogeometric analysis:CAD, finite elements, NURBS, exact geometry and mesh refinement[J]. Comput. Methods Appl. Mech. Engrg., 2005, 194(39-41):4135-4195.[19] Brezzi F, Fortin M, Marini L. Mixed Finite Element Methods with Continuous Stresses[J]. Math. Models Methods Appl. Sci., 1993, 3:275-287.[20] Xie X, Xu J, Xue G. Uniformly stable finite element methods for Darcy-Stokes-Brinkman models[J]. J. Comput. Math., 2008, 26(3):437-455.[21] Bonet J, Wood R. Nonlinear continuum mechanics for finite element analysis[M]. Cambridge University Press, New York, 1997.[22] Brezzi F, Fortin M. Mixed and hybrid finite element methods[M]. Springer-Verlag, New York, 1991.[23] Brezzi F. On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers[J]. RAIRO Anal. Numer., 1974, 8(2):129-151.[24] Arnold D, Brezzi F, Fortin M. A stable finite element for the Stokes equations[J]. Calcolo, 1984, 21(4):337-344.[25] Girault V, Raviart P. Finite element methods for Navier-Stokes equations:theory and algorithms[M]. Springer-Verlag, Berlin-Heidelberg-New York-Tokyo, 1986. |