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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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A posteriori analysis of the finite element discretization of some parabolic equations
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by A. Bergam, C. Bernardi and Z. Mghazli PDF
Math. Comp. 74 (2005), 1117-1138 Request permission

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
  • Received by editor(s): January 19, 2002
  • Received by editor(s) in revised form: January 27, 2004
  • Published electronically: 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 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1117-1138
  • MSC (2000): Primary 65N30, 65N50
  • DOI: https://doi.org/10.1090/S0025-5718-04-01697-7
  • MathSciNet review: 2136996