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Mathematical foundation of the MFS for certain elliptic systems in linear elasticity

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Abstract

The method of fundamental solutions (MFS) is a Trefftz–type technique in which the solution of an elliptic boundary value problem is approximated by a linear combination of translates of fundamental solutions with singularities placed on a pseudo–boundary, i.e., a surface embracing the domain of the problem under consideration. In this work, we develop a mathematical framework for the numerical implementation of the MFS in elliptic systems. We obtain density results, with respect to the C ℓ-norms, which establish the applicability of the method in certain systems arising from the theory of elastostatics and thermo-elastostatics. The domains in our density results may possess holes and they satisfy the segment condition.

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  1. Department of Mathematics and Statistics, University of Cyprus, Kallipoleos 75, P.O. Box 20537, 1678, Nicosia, Cyprus

    Yiorgos-Sokratis Smyrlis

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Correspondence to Yiorgos-Sokratis Smyrlis.

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This work was supported by a grant of the University of Cyprus.

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Smyrlis, YS. Mathematical foundation of the MFS for certain elliptic systems in linear elasticity. Numer. Math. 112, 319–340 (2009). https://doi.org/10.1007/s00211-008-0207-1

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  • DOI: https://doi.org/10.1007/s00211-008-0207-1

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