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$L^{2}$ -error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

Thomas Apel; Dieter Sirch — 2011

Applications of Mathematics

An $L^{2}$ -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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L 2 -error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

$L^{2}$ -error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes