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A posteriori analysis of the finite element discretization of some parabolic equations

Author(s): A. Bergam; C. Bernardi; Z. Mghazli.
Journal: Math. Comp. 74 (2005), 1117-1138.
MSC (2000): Primary 65N30, 65N50
Posted: August 10, 2004
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Abstract: We are interested in the discretization of parabolic equations, either linear or semilinear, by an implicit Euler scheme with respect to the time variable and finite elements with respect to the space variables. The main result of this paper consists of building error indicators with respect to both time and space approximations and proving their equivalence with the error, in order to work with adaptive time steps and finite element meshes.

RÉSUMÉ. Nous considérons la discrétisation d'équations paraboliques, soit linéaires soit semi-linéaires, par un schéma d'Euler implicite en temps et par éléments finis en espace. L'idée de cet article est de construire des indicateurs d'erreur liés à l'approximation en temps et en espace et de prouver leur équivalence avec l'erreur, dans le but de travailler avec des pas de temps adaptatifs et des maillages d'éléments finis adaptés à la solution.

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Additional Information:

A. Bergam
Affiliation: Laboratoire SIANO, Département de Mathématiques et d'Informatique, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Maroc

C. Bernardi
Affiliation: Analyse Numérique, C.N.R.S. & Université Pierre et Marie Curie,B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France

Z. Mghazli
Affiliation: Laboratoire SIANO, Département de Mathématiques et d'Informatique, Faculté des Sciences, Université Ibn Tofail, B.P. 133, Kénitra, Maroc

DOI: 10.1090/S0025-5718-04-01697-7
PII: S 0025-5718(04)01697-7
Keywords: Parabolic equations, finite elements, a posteriori analysis
Received by editor(s): January 19, 2002
Received by editor(s) in revised form: January 27, 2004
Posted: August 10, 2004
Additional Notes: Recherche menée dans le cadre du projet AUPELF-UREF n$^0$ 2000/PAS/38 et de l'A.I. France-Maroc n$^0$ 221/STU/00
Copyright of article: Copyright 2004, American Mathematical Society

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