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A-posteriori error estimates for the finite element method. (English) Zbl 0396.65068

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
74S05 Finite element methods applied to problems in solid mechanics
65L10 Numerical solution of boundary value problems involving ordinary differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
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References:
[1] Hull, SIAM J. Num. Anal. 9 pp 603– (1972)
[2] Shampine, SIAM Rev. 18 pp 376– (1976)
[3] Krogh, J. ACM 4 pp 545– (1973)
[4] and , ’Computational aspects of finite element analysis’, in Mathematical Software–III (Ed. ), Academic Press, New York, 1973, pp. 223-253.
[5] and , ’Error estimates for adaptive finite element computations’, University of Maryland, Institute for Physical Science and Technology, Technical Note BN-854 (1977);
[6] SIAM J. Num. Anal. 15 (1978)
[7] and , Theoretical and Computational Analysis of the Finite Element Method, in preparation.
[8] and , ’Analysis of optimal finite element meshes in R1’, University of Maryland, Institute for Physical Science and Technology, Technical Note BN-869 (1977).
[9] and , ’Survey lectures on the mathematical foundations of the finite element method’, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (Ed. ), Academic Press, New York, 1972.
[10] Sobolev Spaces, Academic Press, New York, 1975. · Zbl 0314.46030
[11] and (Ed.), Modern Numerical Methods for Ordinary Differential Equations, Clarendon Press, Oxford, 1976. · Zbl 0348.65064
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