Numerische Simulation auf massiv parallelen Rechnern

A note on anisotropic interpolation error estimates for isoparametric quadrilateral nite elements Preprint SFB393/96-10 Abstract. Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral Lagrangian nite elements with straight edges. These elements are allowed to have diameters with dierent asymptotic behaviour in dierent space directions. The case of ane elements (parallelepipeds) with arbi-trarily high degree of the shape functions is considered rst. 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 nite element method for a reaction diusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements. AMS(MOS) subject classication. 65D05, 65N30, 65N50 Key Words. Anisotropic nite elements, interpolation error estimate, isoparametric map, reaction diusion problem