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Maximum-norm resolvent estimates for ellipticfinite element operators on nonquasiuniform triangulations

Published online by Cambridge University Press:  16 January 2007

Nikolai Yu. Bakaev ,
Michel Crouzeix  and
Vidar Thomée
Nikolai Yu. Bakaev
Affiliation:
Department of Economic Dynamics, EAI, Moscow Engineering Physics Institute (State University), Kashirskoe Shosse 31, Moscow 115409, Russia. bakaev@postman.ru
Michel Crouzeix
Affiliation:
IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France. michel.crouzeix@univ-rennes1.fr
Vidar Thomée
Affiliation:
Department of Mathematics, Chalmers University of Technology, 41296 Göteborg, Sweden. thomee@math.chalmers.se
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Abstract


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.


Keywords

Resolvent estimatesstabilitysmoothingmaximum-normellipticparabolicfinite elementsnonquasiuniform triangulations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 5 , September 2006 , pp. 923 - 937
Copyright
© EDP Sciences, SMAI, 2007

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References

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