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L 2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes

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Abstract

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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Authors and Affiliations

  1. Institut für Mathematik und Bauinformatik, Universität der Bundeswehr München, 85577, Neubiberg, Germany

    Thomas Apel & Dieter Sirch

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  1. Thomas Apel
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  2. Dieter Sirch
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Correspondence to Thomas Apel.

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This work was supported by the DFG priority program 1253.

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Apel, T., Sirch, D. L 2-error estimates for Dirichlet and Neumann problems on anisotropic finite element meshes. Appl Math 56, 177–206 (2011). https://doi.org/10.1007/s10492-011-0002-7

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  • DOI: https://doi.org/10.1007/s10492-011-0002-7

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