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A note on anisotropic interpolation error estimates for isoparametric quadrilateral finite elements

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 (parallelepipeds) 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.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:ch1-199801071
Date30 October 1998
CreatorsApel, Th.
ContributorsTU Chemnitz, SFB 393
PublisherUniversit├Ątsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formatapplication/pdf, application/postscript, text/plain, application/zip

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