Analysis of a family of HDG methods for second order elliptic problems
Tài liệu tham khảo
Pian, 1964, Derivation of element stiffness matrices by assumed stress distributions, AIAA J., 2, 1333, 10.2514/3.2546
Atluri, 1977, On hybrid finite element models in nonlinear solid mechanics, 3
Pian, 1969, Basis of finite element methods for solid continua, Internat. J. Numer. Methods Engrg., 1, 3, 10.1002/nme.1620010103
Pian, 1972, Finite element formulation by variational principles with relaxed continuity requirements, 671
Pian, 1984, Rational approach for assumed stress finite elements, Internat. J. Numer. Methods Engrg., 20, 1685, 10.1002/nme.1620200911
Pian, 1986, Relations between incompatible displacement model and hybrid stress model, Internat. J. Numer. Methods Engrg., 22, 173, 10.1002/nme.1620220112
Pian, 1988, A rational approach for choosing stress terms for hybrid finite element formulations, Internat. J. Numer. Methods Engrg., 26, 2331, 10.1002/nme.1620261014
Sze, 1992, Efficient formulation of robust hybrid elements using orthogonal stress/strain interpolants and admissible matrix formulation, Internat. J. Numer. Methods Engrg., 35, 1, 10.1002/nme.1620350102
Sze, 1993, Hybrid hexahedral element for solids,plates,shells and beams by selective scaling, Internat. J. Numer. Methods Engrg., 36, 1519, 10.1002/nme.1620360907
Xie, 2004, Optimization of stress modes by energy compatibility for 4-node hybrid quadrilaterals, Internat. J. Numer. Methods Engrg., 59, 293, 10.1002/nme.877
Zhang, 2010, Accurate 8-node hybrid hexahedral elements with energy-compatible stress modes, Adv. Appl. Math. Mech., 2, 333, 10.4208/aamm.09-m0959
Simo, 1990, A class of mixed assumed strain methods and the method of incompatible modes, Internat. J. Numer. Methods Engrg., 29, 1595, 10.1002/nme.1620290802
Reddy, 1995, Stability and convergence of a class of enhanced strain methods, SIAM J. Numer. Anal., 32, 1705, 10.1137/0732077
Kasper, 2000, A mixed-enhanced strain method—part I: Geometrically linear problems, Comput. & Structures, 75, 237, 10.1016/S0045-7949(99)00134-0
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
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
Brezzi, 1991
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
Oden, 1977, Dual-Mixed Hybrid finite element method for second-order elliptic problems, Lecture Notes in Math., 606, 275, 10.1007/BFb0064469
Raviart, 1977, Primal hybrid finite element methods for 2nd order elliptic equations, J. Math. Comput., 31, 391, 10.1090/S0025-5718-1977-0431752-8
Raviart, 1979, Dual finite element models for second order elliptic problems, 175
Ciarlet, 1978
Roberts, 1991, Mixed and hybrid methods, in handbook of numerical analysis, II, 523, 10.1016/S1570-8659(05)80041-9
Cockburn, 2009, Unified hybridization of discontinuous Galerkin, mixed, and conforming Galerkin methods for second order elliptic problems, SIAM J. Numer. Anal., 47, 1319, 10.1137/070706616
Arnold, 1985, Mixed and non-conforming finite element methods: implementation, post-processing and error estimates, Modél. Math. Anal. Numér., 19, 7, 10.1051/m2an/1985190100071
Cockburn, 2004, A characterization of hybridized mixed methods for second order elliptic problems, SIAM J. Numer. Anal., 42, 283, 10.1137/S0036142902417893
Cockburn, 2007, Locally conservative fluxes for the continuous Galerkin method, SIAM J. Numer. Anal., 45, 1742, 10.1137/060666305
Cockburn, 2010, A projection-based error analysis of HDG methods, Math. Comp., 79, 1351, 10.1090/S0025-5718-10-02334-3
Cockburn, 2012, Conditions for superconvergence of HDG methods for second-order elliptic problems, Math. Comp., 81, 1327, 10.1090/S0025-5718-2011-02550-0
Lehrenfeld, 2010
Qiu
Gudi, 2010, A new error analysis for discontinuous finite element methods for linear elliptic problems, Math. Comp., 79, 2169, 10.1090/S0025-5718-10-02360-4
Adams, 2003
Cockburn, 2009, Superconvergent discontinuous Galerkin methods for second-order elliptic problems, Math. Comp., 78, 1, 10.1090/S0025-5718-08-02146-7
