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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 ThoméeDepartment 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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