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An error estimate for the truncation method for the solution of parabolic obstacle variational inequalities. (English) Zbl 0367.65056


MSC:

65N15 Error bounds for boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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[1] Alan E. Berger, The truncation method for the solution of a class of variational inequalities, Rev. Française Automat. Informat. Recherche Opérationnelle Sér. \jname RAIRO Analyse Numérique 10 (1976), no. R-1, 29 – 42 (English, with Loose French summary). · Zbl 0334.49012
[2] Alan E. Berger, Melvyn Ciment, and Joel C. W. Rogers, Numerical solution of a diffusion consumption problem with a free boundary, SIAM J. Numer. Anal. 12 (1975), no. 4, 646 – 672. · Zbl 0317.65032 · doi:10.1137/0712049
[3] Haïm Brézis, Problèmes unilatéraux, J. Math. Pures Appl. (9) 51 (1972), 1 – 168. · Zbl 0221.35028
[4] G. Duvaut and J.-L. Lions, Les inéquations en mécanique et en physique, Dunod, Paris, 1972 (French). Travaux et Recherches Mathématiques, No. 21. · Zbl 0298.73001
[5] Richard S. Falk, Error estimates for the approximation of a class of variational inequalities, Math. Comput. 28 (1974), 963 – 971. · Zbl 0297.65061
[6] R. FALK, Unpublished manuscript.
[7] Charles Hunt and Nabil Nassif, Inéquations variationnelles et détermination de la charge d’espace de certains semi-conducteurs, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1409 – 1412 (French). · Zbl 0283.49020
[8] Claes Johnson, A convergence estimate for an approximation of a parabolic variational inequality, SIAM J. Numer. Anal. 13 (1976), no. 4, 599 – 606. · Zbl 0337.65055 · doi:10.1137/0713050
[9] J.-L. Lions, Quelques problèmes de la théorie des équations non linéaires d’évolution, Problems in non-linear analysis (C.I.M.E., IV Ciclo, Varenna, 1970), Edizioni Cremonese, Rome, 1971, pp. 189 – 342 (French).
[10] J. NEČAS, Les Méthodes Directes en Théorie des Equations Elliptiques, Masson, Paris; Academia, Prague, 1967. MR 37 #3168. · Zbl 1225.35003
[11] Gilbert Strang, Approximation in the finite element method, Numer. Math. 19 (1972), 81 – 98. · Zbl 0221.65174 · doi:10.1007/BF01395933
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