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Estimations a posteriori d’un schéma de volumes finis pour un problème non linéaire

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Summary.

RésuméDans cet article, nous développons des estimations a posteriori de l’erreur commise en approchant un problème elliptique non linéaire, par une Méthode de Volumes Finis (MVF) de type ‚‚Vertex-Centered’’. Les estimateurs obtenus mesurent, le résidu de l’équation forte et l’irrégularité de la solution discrète, qui se traduit par des sauts à travers les inter-élélments. Une condition sur la fonction flux numérique sera imposée pour traiter la non conformité du problème, au cours de l’évaluation de l’estimation.

Summary.We derive a posteriori error estimates for vertex-centered finite volume discretizations of a class of non-linear elliptic pdes. The error estimates are of residual type and incorporate residuals of the pde in its strong form on the control volumes and jumps of the pde’s prinicipal part across the element boundaries. The non-conformity of the discretization is taken into account by a condition on the numerical flux function.

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Authors and Affiliations

  1. Laboratoire SIANO, Département de Maths et d’Informatique, Faculté des sciences, Université Ibn Tofail, 133, Kénitra, Maroc

    A. Bergam & Z. Mghazli

  2. Ruhr-Universität, Bochum, Fakultät für Mathematik, 44780, Bochum, Germany

    R. Verfürth

Authors
  1. A. Bergam
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  2. Z. Mghazli
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  3. R. Verfürth
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Correspondence to Z. Mghazli.

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Mathematics Subject Classification (2000): 35J60, 65N15, 65N30, 65N50, 74S10

Recherche menée dans le cadre du projet AUPELF-FICU N° 2000/PAS/38 et du projet DAAD

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Bergam, A., Mghazli, Z. & Verfürth, R. Estimations a posteriori d’un schéma de volumes finis pour un problème non linéaire. Numer. Math. 95, 599–624 (2003). https://doi.org/10.1007/s00211-003-0460-2

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  • DOI: https://doi.org/10.1007/s00211-003-0460-2

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