L2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

被引：0
|
作者：
Thomas Apel
Dieter Sirch
机构：
[1] Universität der Bundeswehr München,Institut für Mathematik und Bauinformatik
来源：
Applications of Mathematics | 2011年 / 56卷
关键词：
elliptic boundary value problem; a priori error estimates; interpolation of nonsmooth functions; finite element error; non-convex domains; edge singularities; anisotropic mesh grading; 65D05; 65N30;
D O I：
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摘要：
An L2-estimate of the finite element error is proved for a Dirichlet and a Neumann boundary value problem on a three-dimensional, prismatic and non-convex domain that is discretized by an anisotropic tetrahedral mesh. To this end, an approximation error estimate for an interpolation operator that is preserving the Dirichlet boundary conditions is given. The challenge for the Neumann problem is the proof of a local interpolation error estimate for functions from a weighted Sobolev space.
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