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Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2006

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

Résumé

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.
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Dates et versions

hal-00364463 , version 1 (30-11-2017)

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Nikolai Yu Bakaev, Michel Crouzeix, Vidar Thomée. Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations. ESAIM: Mathematical Modelling and Numerical Analysis, 2006, 40 (5), pp.923-937. ⟨10.1051/m2an:2006040⟩. ⟨hal-00364463⟩
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