2 . Notation and Results for Affine Elements 11
نویسنده
چکیده
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 diierent asymptotic behaviour in diierent space directions. The case of aane elements (parallelepipeds) with arbitrarily 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 diiusion problem in a polygonal domain is considered. The boundary layers are resolved using anisotropic trapezoidal elements.
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