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Multilevel particle-partition of unity method

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Abstract

This paper is concerned with the particle-partition of unity method, a meshfree generalization of the finite element method. We present the fundamental construction principles and abstract approximation properties of the resulting function spaces V PU. Moreover, we discuss the construction of optimal approximation spaces for a reference application in linear elastic fracture mechanics in particular. The presented construction not only yields optimal convergence rates globally independently of the regularity of the solution, our method shows a super-convergence near the singular points of the solution.

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  1. Institut für Parallele und Verteilte Systeme, Universität Stuttgart, Stuttgart, Germany

    Marc Alexander Schweitzer

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  1. Marc Alexander Schweitzer
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Correspondence to Marc Alexander Schweitzer.

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M. A. Schweitzer was supported in part by the Sonderforschungsbereich 611 Singular phenomena and scaling in mathematical models funded by the Deutsche Forschungsgemeinschaft.

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Schweitzer, M.A. Multilevel particle-partition of unity method. Numer. Math. 118, 307–328 (2011). https://doi.org/10.1007/s00211-010-0346-z

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  • DOI: https://doi.org/10.1007/s00211-010-0346-z

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