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Optimal a priori estimates for interface problems

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Summary.

We consider a priori estimates in weighted norms for interface problems with piecewise constant diffusion constants which do not depend on the ratio between the constants. Our result generalizes an estimate of Lemrabet to arbitrary dimensions and includes curved boundaries. Furthermore, we discuss criteria for the existence of a uniform Poincaré estimate in weighted norms. In the affirmative case we obtain a robust finite element error bound in weighted norms. Finally, we present numerical experiments including a case with no uniform Poincaré constant.

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Authors and Affiliations

  1. Mathematisches Institut I, Universität Karlsruhe, Kaiserstr. 12, 76128, Karlsruhe, Germany

    Michael Plum

  2. Institut fu˜r Angewandte Mathematik, Universität Erlangen-Nürnberg, Martensstr. 3, 91058, Erlangen, Germany

    Christian Wieners

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  1. Michael Plum
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  2. Christian Wieners
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Correspondence to Christian Wieners.

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Mathematics Subject Classification (1991): 65N15, 65N20

Supported in part by the Deutsche Forschungsgemeinschaft, SFB 404

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Plum, M., Wieners, C. Optimal a priori estimates for interface problems. Numer. Math. 95, 735–759 (2003). https://doi.org/10.1007/s002110200395

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