| Issue |
ESAIM: M2AN
Volume 40, Number 5, September-October 2006
|
|
|---|---|---|
| Page(s) | 923 - 937 | |
| DOI | https://doi.org/10.1051/m2an:2006040 | |
| Published online | 16 January 2007 | |
Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
1
Department of Economic Dynamics, EAI, Moscow Engineering Physics
Institute (State University), Kashirskoe Shosse 31, Moscow 115409,
Russia. bakaev@postman.ru
2
IRMAR,
Université de Rennes I,
Campus de Beaulieu,
35042 Rennes Cedex, France.
michel.crouzeix@univ-rennes1.fr
3
Department of Mathematics,
Chalmers University of Technology,
41296 Göteborg, Sweden.
thomee@math.chalmers.se
Received:
2
May
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.
Mathematics Subject Classification: 65M06 / 65M12 / 65M60
Key words: Resolvent estimates / stability / smoothing / maximum-norm / elliptic / parabolic / finite elements / nonquasiuniform triangulations.
© EDP Sciences, SMAI, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.