Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
Department of Economic Dynamics, EAI, Moscow Engineering Physics
Institute (State University), Kashirskoe Shosse 31, Moscow 115409,
2 IRMAR, Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex, France. email@example.com
3 Department of Mathematics, Chalmers University of Technology, 41296 Göteborg, Sweden. firstname.lastname@example.org
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.
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