Free access article

ESAIM: Proc., 2007, Vol. 21, pp. 98-107
DOI: 10.1051/proc:072108

Maximum-Norm Stability, Smoothing and Resolvent Estimates for Parabolic Finite Element Equations

Vidar Thomée

Department of mathematics, Chalmers University of Technology, S 412 96 Göteborg, Sweden;
    e-mail: thomee@math.chalmers.se

(September 27, 2006 / Published online: 4 December 2007)

Abstract
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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