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Adaptive finite element methods in computational mechanics. (English) Zbl 0778.73071
Summary: We present a general approach to adaptivity for finite element methods and give applications to linear elasticity, nonlinear elasto-plasticity and nonlinear conservation laws, including numerical results.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
74C99 Plastic materials, materials of stress-rate and internal-variable type
35L65 Hyperbolic conservation laws
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[1] Eriksson, K., Adaptive finite element methods based on optimal error estimates for linear elliptic problems, ()
[2] Eriksson, K.; Johnson, C., Adaptive finite element methods for parabolic problems I: A linear model problem, SIAM J. numer. anal., 28, 43-77, (1991) · Zbl 0732.65093
[3] Eriksson, K.; Johnson, C., Adaptive finite element methods for parabolic problems II: A priori error estimates in L−8(L2), ()
[4] Eriksson, K.; Johnson, C., Adaptive finite element methods for parabolic problems III: time steps variable in space and non-coercive problems, ()
[5] Eriksson, K.; Johnson, C., Adaptive finite element methods for parabolic problems IV: non-linear problems, ()
[6] K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for stationary convection diffusion problems, Math. Comp., in press. · Zbl 0795.65074
[7] K. Eriksson and C. Johnson, Adaptive streamline diffusion finite element methods for time-dependent convection-diffusion problems, to appear. · Zbl 0795.65074
[8] Eriksson, K.; Johnson, C., An adaptive finite element method for linear elliptic problems, Math. comp., 50, 361-383, (1988) · Zbl 0644.65080
[9] Eriksson, K.; Johnson, C., Error estimates and automatic time step control for nonlinear parabolic problems, I, SIAM J. numer. anal., 24, 12-23, (1987) · Zbl 0618.65104
[10] Johnson, C., Error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations, SIAM J. numer. anal., 25, 908-926, (1988) · Zbl 0661.65076
[11] Johnson, C., Adaptive finite element methods for diffusion and convection problems, Comput. methods appl. mech. engrg., 82, 301-322, (1990) · Zbl 0717.76078
[12] Johnson, C., Adaptive finite element methods for the obstacle problem, (), to appear in M^3AS. · Zbl 0767.65056
[13] Johnson, C.; Hansbo, P., Adaptive finite element methods for small strain elasto-plasticity, (), in press.
[14] Johnson, C., Discontinuous Galerkin finite element methods for second order hyperbolic problems, (), to appear in Comput. Methods Appl. Mech. Engrg. · Zbl 0787.65070
[15] Hansbo, P.; Johnson, C., Adaptive streamline diffusion methods for compressible flow using conservation variables, Comput. methods appl. mech. engrg., 87, 267-280, (1991) · Zbl 0760.76046
[16] C. Johnson and A. Szepessy, Adaptive streamline diffusion methods for conservation laws, to appear. · Zbl 0685.65086
[17] Johnson, C., A new approach to algorithms for convection problems which are based on exact transport + projection, Comput. methods appl. mech. engrg., 100, 45-62, (1992) · Zbl 0825.76413
[18] Babuška, I.; Rheinboldt, W.C., A posteriori error estimators for the finite element method, Internat. J. numer. methods engrg., 12, 1597-1615, (1978) · Zbl 0396.65068
[19] Babuška, I., Feedback, adaptivity and a posteriori estimates in finite elements: aims, theory, and experience, (), 3-23
[20] Bank, R.; Weiser, A., Some a posteriori error estimators for elliptic partial differential equations, Math. comp., 44, 283-301, (1985) · Zbl 0569.65079
[21] Oden, J.T.; Demkowicz, L.; Rachowicz, W.; Westermann, T.A., Toward a universal h-p adaptive finite element strategy, part 2. A posteriori error estimation, Comput. methods appl. mech. engrg., 77, 113-180, (1989) · Zbl 0723.73075
[22] Zienkiewicz, O.C.; Zhu, J.Z., A simple error estimator and adaptive procedure for practical engineering analysis, Internat. J. numer. methods engrg., 24, 337-357, (1987) · Zbl 0602.73063
[23] Ainsworth, M.; Zhu, J.Z.; Craig, A.W.; Zienkiewicz, O.C., Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method, Internat. J. numer. methods engrg., 28, 2161-2174, (1989) · Zbl 0716.73082
[24] Verfürth, R., A posteriori error estimators for the Stokes equation, Numer. math., 55, 309-325, (1989) · Zbl 0674.65092
[25] Rank, E.; Zienkiewicz, O.C., A simple error estimator in the finite element method, Comm. appl. numer. methods, 3, 243-249, (1987) · Zbl 0623.65120
[26] Peraire, J.; Vahdati, M.; Morgan, K.; Zienkiewicz, O.C., Adaptive remeshing for compressible flow computations, J. comput. phys., 72, 449-466, (1987) · Zbl 0631.76085
[27] Simo, J.C., A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects, Comput. methods appl. mech. engrg., 68, 1-31, (1988) · Zbl 0644.73043
[28] Temam, R., Mathematical problems in plasticity, (1985), Gauthier-Villars Paris · Zbl 0457.73017
[29] Jespersen, D., Ritz-Galerkin methods for singular boundary value problems, SIAM J. numer. anal., 15, 813-834, (1978) · Zbl 0393.65043
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