Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods
Tài liệu tham khảo
Babuska, 1977, Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems, Comput. Methods Appl. Mech. Engrg., 11, 175, 10.1016/0045-7825(77)90058-5
Babuška, 1992, On locking and robustness in the finite element method, SIAM J. Numer. Anal., 29, 1261, 10.1137/0729075
Bernardi, 1998, A local regularization operator for triangular and quadrilateral finite elements, SIAM J. Numer. Anal., 35, 1893, 10.1137/S0036142995293766
Braess, 1998, Enhanced assumed strain elements and locking in membrane problems, Comput. Methods Appl. Mech. Engrg., 165, 155, 10.1016/S0045-7825(98)00037-1
Braess, 2004, Uniform convergence and a posteriori error estimators for the enhanced strain finite element method, Numer. Math., 96, 461, 10.1007/s00211-003-0486-5
Bramble, 2001, Least-squares methods for linear elasticity based on a discrete minus one inner product, Comput. Methods Appl. Mech. Engrg., 191, 727, 10.1016/S0045-7825(01)00255-9
Brezzi, 1974, On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. Rouge, 8, 129
Brezzi, 1991
Carstensen, 2005, A unifying theory of a posteriori finite element error control, Numer. Math., 100, 617, 10.1007/s00211-004-0577-y
Carstensen, 2007, Framework for the a posteriori error analysis of nonconforming finite elements, SIAM J. Numer. Anal., 45, 68, 10.1137/050628854
Carstensen, 2011, A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner–Mindlin plates, Comput. Methods Appl. Mech. Engrg., 200, 1161, 10.1016/j.cma.2010.06.035
Ciarlet, 1978
Lesaint, 1976, On the convergence of Wilson’s nonconforming element for solving the elastic problems, Comput. Methods Appl. Mech. Engrg., 7, 1, 10.1016/0045-7825(76)90002-5
Lesaint, 1980, Convergence of the nonconforming Wilson element for arbitrary quadrilateral meshes, Numer. Math., 36, 33, 10.1007/BF01395987
Oden, 1976, Theory of mixed and hybrid finite-element approximations in linear elasticity, Appl. Methods Funct. Anal. Problems Mech., 90, 10.1007/BFb0088747
Oden, 1976, vol. 79
Pian, 1964, Derivation of element stiffness matrices by assumed stress distributions, AIAA J., 2, 1333, 10.2514/3.2546
Pian, 1982, Alternative ways for formulation of hybrid stress elements, Int. J. Numer. Methods Engrg., 18, 1679, 10.1002/nme.1620181107
Pian, 1984, Rational approach for assumed stress finite elements, Int. J. Numer. Methods Engrg., 20, 1685, 10.1002/nme.1620200911
Pian, 1986, Relations between incompatible displacement model and hybrid stress model, Int. J. Numer. Methods Engrg., 22, 173, 10.1002/nme.1620220112
Pian, 1988, A rational approach for choosing stress terms for hybrid finite element formulations, Int. J. Numer. Methods Engrg., 26, 2331, 10.1002/nme.1620261014
Piltner, 2000, An alternative version of the Pian–Sumihara element with a simple extension to non-linear problems, Comput. Mech., 26, 483, 10.1007/s004660000198
Piltner, 1995, A quadrilateral mixed finite element with two enhanced strain modes, Int. J. Numer. Methods Engrg., 38, 1783, 10.1002/nme.1620381102
Piltner, 1999, A systematic construction of B-bar functions for linear and non-linear mixed-enhanced finite elements for plane elasticity problems, Int. J. Numer. Methods Engrg., 44, 615, 10.1002/(SICI)1097-0207(19990220)44:5<615::AID-NME518>3.0.CO;2-U
Raviart, 1977, A mixed finite element method for 2-nd order elliptic problems, Math. Aspects Finite Elem. Methods, 292, 10.1007/BFb0064470
Reddy, 1995, Stability and convergence of a class of enhanced strain methods, SIAM J. Numer. Anal., 32, 1705, 10.1137/0732077
Shi, 1984, A convergence condition for the quadrilateral Wilson element, Numer. Math., 44, 349, 10.1007/BF01405567
Simo, 1990, A class of mixed assumed strain methods and the method of incompatible modes, Int. J. Numer. Methods Engrg., 29, 1595, 10.1002/nme.1620290802
Taylor, 1976, A non-conforming element for stress analysis, Int. J. Numer. Methods Engrg., 10, 1211, 10.1002/nme.1620100602
Verfürth, 1999, A review of a posteriori error estimation techniques for elasticity problems, Comput. Methods Appl. Mech. Engrg., 176, 419, 10.1016/S0045-7825(98)00347-8
Wilson, 1973, Incompatible displacement models, Numer. Comput. Methods Struct. Mech., 43, 10.1016/B978-0-12-253250-4.50008-7
Xie, 2005, An accurate hybrid macro-element with linear displacements, Commun. Numer. Methods Engrg., 21, 1, 10.1002/cnm.721
Xie, 2011, New mixed finite elements for plane elasticity and stokes equations, Sci. China Math., 54, 10.1007/s11425-011-4171-3
Xie, 2004, Optimization of stress modes by energy compatibility for 4-node hybrid quadrilaterals, Int. J. Numer. Methods Engrg., 59, 293, 10.1002/nme.877
Xie, 2008, Accurate 4-node quadrilateral elements with a new version of energy-compatible stress mode, Commun. Numer. Methods Engrg., 24, 125, 10.1002/cnm.962
Yeo, 1996, Equivalence between enhanced assumed strain method and assumed stress hybrid method based on the Hellinger–Reissner principle, Int. J. Numer. Methods Engrg., 39, 3083, 10.1002/(SICI)1097-0207(19960930)39:18<3083::AID-NME996>3.0.CO;2-F
Zhang, 1997, Analysis of some quadrilateral nonconforming elements for incompressible elasticity, SIAM J. Numer. Anal., 34, 640, 10.1137/S0036142995282492
Zhou, 2001, Combined hybrid approach to finite element schemes of high performance, Int. J. Numer. Methods Engrg., 51, 181, 10.1002/nme.151
Zhou, 2002, A unified analysis for stress/strain hybrid methods of high performance, Comput. Methods Appl. Mech. Engrg., 191, 4619, 10.1016/S0045-7825(02)00396-1
