A posteriori error estimation in finite element analysis

Computer Methods in Applied Mechanics and Engineering - Tập 142 Số 1-2 - Trang 1-88 - 1997
Mark Ainsworth1, J. Tinsley Oden2
1Department of Mathematics, University of Leicester, Leicester, UK
2Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX 78712, USA

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Adams, 1978, Vol. 65

Ainsworth, 1994, The performance of Bank-Weiser's error estimator for quadrilateral finite elements, Numer. Methods PDE 10, 609, 10.1002/num.1690100508

M. Ainsworth, The influence and selection of subspaces for a posteriori error estimators, Numer. Math, (to appear).

Ainsworth, 1991, A posteriori error estimators in the finite element method, Numer. Math., 60, 429, 10.1007/BF01385730

Ainsworth, 1993, A posteriori error estimators for second order elliptic systems Part 2. An optimal order process for calculating self equilibrating fluxes, Comput. Math. Appl., 26, 75, 10.1016/0898-1221(93)90007-I

Ainsworth, 1993, A unified approach to a posteriori error estimation based on element residual methods, Numer. Math., 65, 23, 10.1007/BF01385738

M. Ainsworth and J.T. Oden, A posteriori error estimates for Stokes' and Oseen's equations, SIAM J. Numer. Anal, (to appear).

Ainsworth, 1993, Local a posteriori error estimators for variational inequalities, Numer. Methods PDE, 9, 23, 10.1002/num.1690090104

Aubin, 1970, Some aspects of the method of the hypercircle applied to elliptic variational problems

Babuska, 1987, A feedback finite element method with a posteriori error estimation Part 1, Comput. Methods Appl. Mech. Engrg., 61, 1, 10.1016/0045-7825(87)90114-9

Babuska, 1978, Error estimates for adaptive finite element computations, SIAM J. Numer. Anal., 18, 736, 10.1137/0715049

Babuska, 1981, A posteriori error analysis of finite element solutions for one dimensional problems, SIAM J. Numer. Anal., 18, 565, 10.1137/0718036

Babuska, 1978, A posteriori error estimates for the finite element method, Int. J. Numer. Methods Engrg., 12, 1597, 10.1002/nme.1620121010

Babuska, 1979, Analysis of optimal finite element meshes in R1, Math. Comput., 33, 435

Babuska, 1994, A model study of the quality of a posteriori estimators for linear elliptic problems error estimation in the interior of patchwise uniform grids of triangles, Comput. Methods Appl. Mech. Engrg., 114, 307, 10.1016/0045-7825(94)90177-5

Babuska, 1994, Validation of a posteriori error estimators by a numerical approach, Int. J. Numer. Methods Engrg., 37, 1073, 10.1002/nme.1620370702

Babuska, 1987, The optimal convergence rate of the p version of the finite element method, SIAM J. Numer. Anal., 24, 750, 10.1137/0724049

Babuska, 1981, The p version of the finite element method, SIAM J. Numer. Anal., 18, 512, 10.1137/0718033

Babuska, 1986, Asymptotically exact a posteriori error estimator for biquadratic elements

Babuska, 1986

Bank, 1991, A posteriori error estimates for the Stokes problem, SIAM J. Numer. Anal., 28, 591, 10.1137/0728033

Bank, 1986, Analysis of a local a posteriori error estimate for elliptic equations, 119

Bank, 1985, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput., 44, 283, 10.1090/S0025-5718-1985-0777265-X

Baranger, 1991, Estimateurs a posteriori d'erreur pour le calcul adaptatif d'ecoulements quasi-Newtoniens, RAIRO Anal. Numér., 25, 31

Ciarlet, 1978

Clément, 1975, Approximation by finite element functions using local regularization, RAIRO Anal. Numér., 2, 77

de Veubeke, 1965, Displacement and equilibrium models in the finite element method

Demkowicz, 1985, On an h-type mesh refinement strategy based on minimization of interpolation errors, Comput. Methods Appl. Mech. Engrg., 53, 67, 10.1016/0045-7825(85)90076-3

Demkowicz, 1984, Adaptive finite elements for flow problems with moving boundaries. Part 1: Variational principles and a posteriori error estimates, Comput. Methods Appl. Mech. Engrg., 46, 217, 10.1016/0045-7825(84)90063-X

Demkowicz, 1985, An adaptive p-version finite element method for transient flow problems with moving boundaries, 291

Duran, 1992, On the asymptotic exactness of Bank-Weiser's estimator, Numer. Math., 62, 297, 10.1007/BF01396231

Eriksson, 1987, Error-estimates and automatic time step control for nonlinear parabolic problems, SIAM J. Numer. Anal., 24, 12, 10.1137/0724002

Eriksson, 1991, Adaptive finite-element methods for parabolic problems. Part 1. A linear-model problem, SIAM J. Numer. Anal., 28, 43, 10.1137/0728003

Eriksson, 1995, Adaptive finite-element methods for parabolic problems. Part 2. Optimal error estimates in L∞L2 and L∞L∞, SIAM J. Numer. Anal., 32, 10.1137/0732033

Ewing, 1990, A posteriori error estimation, Comput. Methods Appl. Mech. Engrg., 82, 59, 10.1016/0045-7825(90)90158-I

Girault, 1986, Finite Element Methods for Navier Stokes Equations, Vol. 5

Hlavacek, 1980, Solution of Variational Inequalities in Mechanics, Vol. 66

Johnson, 1992, Adaptive finite element methods in computational mechanics, Comput. Methods Appl. Mech. Engrg., 101, 143, 10.1016/0045-7825(92)90020-K

Kelly, 1984, The self-equilibration of residuals and complementary a posteriori error estimates in the finite element method, Int. J. Numer. Methods Engrg., 20, 1491, 10.1002/nme.1620200811

Kelly, 1983, A posteriori error analysis and adaptive processes in the finite element method. Part I—Error analysis, Int. J. Numer. Methods Engrg., 19, 1593, 10.1002/nme.1620191103

Kinderlehrer, 1980

Krizek, 1987, On superconvergence techniques, Acta Applic. Math., 9, 175, 10.1007/BF00047538

Ladeveze, 1983, Error estimate procedure in the finite element method and applications, SIAM J. Numer. Anal., 20, 485, 10.1137/0720033

Lesaint, 1979, Superconvergence of the gradient of finite element solutions, RAIRO Anal. Numér., 13, 139, 10.1051/m2an/1979130201391

Noor, 1987, Quality assessment and control of finite element solutions, Finite Elem. Des., 3, 1, 10.1016/0168-874X(87)90030-8

Oden, 1987, Advances in adaptive improvements: A survey of adaptive finite element methods in computational mechanics, 1

Oden, 1989, Toward a universal h-p adaptive finite element strategy. Part 2 A posteriori error estimation, Comput. Methods Appl. Mech. Engrg., 77, 113, 10.1016/0045-7825(89)90130-8

Oden, 1986, Adaptive methods for problems in solid and fluid mechanics, 249

Oden, 1994, A posteriori error estimators for the Navier-Stokes problem, Comput. Methods Appl. Mech. Engrg., 111, 185, 10.1016/0045-7825(94)90045-0

Peraire, 1987, Adaptive remeshing for compressible flow computations, J. Comput. Phys., 72, 449, 10.1016/0021-9991(87)90093-3

Raviart, 1977, Primal hybrid finite element methods for 2nd order elliptic equations, Math. Comput., 31, 391, 10.1090/S0025-5718-1977-0431752-8

Scott, 1992, Finite element interpolation of non-smooth functions satisfying boundary conditions, Math. Comput., 54, 483, 10.1090/S0025-5718-1990-1011446-7

Stein, 1970

Szabo, 1986, Estimation and control of error based on p convergence, 61

Szabo, 1986, Mesh design for the p version of the finite element, Comput. Methods Appl. Mech. Engrg., 55, 181, 10.1016/0045-7825(86)90091-5

Verfürth, 1989, A posteriori error estimators for the Stokes equations, Numer. Math., 55, 309, 10.1007/BF01390056

Verfürth, 1994, A posteriori error estimation and adaptive mesh refinement techniques, J. Comput. Appl. Math., 50, 67, 10.1016/0377-0427(94)90290-9

Wu, 1993, h-p Adaptive methods for incompressible viscous flow problems

Zienkiewicz, 1983, The hierarchical concept in the finite element method, Comput. Struct., 16, 53, 10.1016/0045-7949(83)90147-5

Zienkiewicz, 1987, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Engrg., 24, 337, 10.1002/nme.1620240206

Zienkiewicz, 1992, The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique, Int. J. Numer. Methods Engrg., 33, 1331, 10.1002/nme.1620330702

Zienkiewicz, 1992, The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity, Int. J. Numer. Methods Engrg., 33, 1365, 10.1002/nme.1620330703

Zlamal, 1975, Some superconvergence results in the finite element method

Zlamal, 1978, Superconvergence and reduced integration in the finite element method, Math. Comput., 32, 663, 10.2307/2006479