Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
Journal article, 2006

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.

elliptic

nonquasiuniform triangulations.

Resolvent estimates

maximum-norm

finite elements

smoothing

stability

parabolic

Author

Vidar Thomee

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Nikolai Yu. Bakaev

Michel Crouzeix

Mathematical Modelling and Numerical Analysis

0764-583X (ISSN) 1290-3841 (eISSN)

Vol. 40 5 923-937

Subject Categories

Computational Mathematics

More information

Created

10/8/2017