Issue |
ESAIM: Proc.
Volume 21, 2007
Journées d'analyse fonctionnelle et numérique en l'honneur de Michel Crouzeix
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Page(s) | 98 - 107 | |
DOI | https://doi.org/10.1051/proc:072108 | |
Published online | 04 December 2007 |
Maximum-Norm Stability, Smoothing and Resolvent Estimates for Parabolic Finite Element Equations
Department of mathematics, Chalmers University of Technology, S 412 96 Göteborg, Sweden; e-mail: thomee@math.chalmers.se
We survey work on stability and smoothing estimates in maximum-norm for spatially semidiscrete finite element approximations of a model parabolic equation, and related such estimates for the resolvent of the corresponding discrete elliptic operator. We end with a short discussion of stability of fully discrete time stepping methods.
Résumé
Nous présentons un bilan des résultats sur la stabilité et les effets régularisants, vus en norme du maximum, lors de la semi-discrétisation éléments finis d'un problème parabolique modèle. Nous montrons le lien avec les estimations de résolvante pour l'opérateur elliptique approché correspondant. Nous concluons par une considération rapide de la discrétisation totale.
Mathematics Subject Classification: 65M12 / 65M60
Key words: finite elements / stability / smoothing / resolvent / maximum-norm / analytic semigroup
© EDP Sciences, ESAIM, 2007
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