, Volume 60, Issue 2, pp 157–174

Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements

  • Th. Apel


Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian finite elements with straight edges. These elements are allowed to have diameters with different asymptotic behaviour in different space directions. The case of affine elements (parallel-epipeds) with arbitrarily high degree of the shape functions is considered first. Then, a careful examination of the multi-linear map leads to estimates for certain classes of more general, isoparametric elements. As an application, the Galerkin finite element method for a reaction diffusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.

AMS Subject Classifications

65D05 65N30 65N50 

Key words

Anisotropic finite elements interpolation error estimate isoparametric map reaction diffusion problem 


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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Th. Apel
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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