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Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations

Vidar Thomée (Institutionen för matematiska vetenskaper, matematik) ; Nikolai Yu. Bakaev ; Michel Crouzeix
M2AN Math. Model. Numer. Anal. (0764-583X ). Vol. 40 (2006), 5, p. 923-937.
[Artikel, refereegranskad vetenskaplig]

In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under weaker conditions on the triangulations than quasiuniformity. In the two-dimensional case, the bound for the resolvent contains a logarithmic factor.

Nyckelord: Resolvent estimates, stability, smoothing, maximum-norm, elliptic, parabolic, finite elements, nonquasiuniform triangulations.



Denna post skapades 2007-12-05. Senast ändrad 2010-01-26.
CPL Pubid: 62502

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Numerisk analys

Chalmers infrastruktur