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The box method for elliptic interface problems on locally refined meshes

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Adaptive Methods — Algorithms, Theory and Applications

Part of the book series: Notes on Numerical Fluid Mechanics (NNFM) ((NONUFM))

Abstract

Consider some second order elliptic boundary value problem of the plane, where the solution involves singularities due to interfaces containing corners or intersecting the boundary of the given domain. The box method is applied to these problems and some results concerning the numerical treatment of interface singularities by appropriate local mesh refinement are presented. For triangular meshes with grading, basic inequalities for norms of grid functions on such meshes and some analytic and matrix properties of the box approximation operator are discussed. Finally, a priori error estimates on locally refined triangular meshes are derived, which yield the same rate of convergence as known for regular solutions.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Chemnitz-Zwickau, PSF 964, D - 09009, Chemnitz, Germany

    Bernd Heinrich

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  1. Bernd Heinrich
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Wolfgang Hackbusch Gabriel Wittum

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© 1994 Springer Fachmedien Wiesbaden

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Heinrich, B. (1994). The box method for elliptic interface problems on locally refined meshes. In: Hackbusch, W., Wittum, G. (eds) Adaptive Methods — Algorithms, Theory and Applications. Notes on Numerical Fluid Mechanics (NNFM). Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14246-1_12

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  • DOI: https://doi.org/10.1007/978-3-663-14246-1_12

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-528-07646-7

  • Online ISBN: 978-3-663-14246-1

  • eBook Packages: Springer Book Archive

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