Anisotropic Interpolation Error Estimates for isoparametric Quadrilateral Finite Elements

摘要

Anisotropic local interpolation error estimates are derived for quadrilateral and hexahedral La- grangian 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.