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

Bakaev, N. Y., Crouzeix, M. & Thomee, V., 2006, In : Esaim-Mathematical modelling and numerical analysis-Modelisation mathematique et analyse numerique. 40, 5, p. 923-937 15 p.

Research output: Contribution to journalArticleAcademicpeer-review

  • Nikolai Yu. Bakaev
  • Michel Crouzeix
  • Vidar Thomee

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.

Original languageEnglish
Pages (from-to)923-937
Number of pages15
JournalEsaim-Mathematical modelling and numerical analysis-Modelisation mathematique et analyse numerique
Issue number5
Publication statusPublished - 2006


  • resolvent estimates, stability, smoothing, maximum, norm, elliptic, parabolic, finite elements, nonquasiuniform triangulations, STABILITY, EQUATIONS, SEMIGROUPS

ID: 4516677