Article
MSC:
35J25,
65D05,
65N15,
65N30,
65N50 | MR 2810243 | Zbl 1224.65252 | DOI: 10.1007/s10492-011-0002-7
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Keywords:
elliptic boundary value problem; a priori error estimates; interpolation of non-smooth functions; finite element error; non-convex domains; edge singularities; anisotropic mesh grading; Dirichlet and a Neumann boundary value problem
elliptic boundary value problem; a priori error estimates; interpolation of non-smooth functions; finite element error; non-convex domains; edge singularities; anisotropic mesh grading; Dirichlet and a Neumann boundary value problem
Summary:
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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