, Volume 60, Issue 2, pp 157–174

Anisotropic interpolation error estimates for isoparametric quadrilateral finite elements

  • Th. Apel

DOI: 10.1007/BF02684363

Cite this article as:
Apel, T. Computing (1998) 60: 157. doi:10.1007/BF02684363


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


Key words

Anisotropic finite elementsinterpolation error estimateisoparametric mapreaction diffusion problem

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

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