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Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem

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Meshfree Methods for Partial Differential Equations V

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 79))

Summary

A vectorial interpolation problem is considered. In addition to the interpolation conditions taken at discrete points, a global, divergence-free condition is also prescribed. Utilizing the idea of the multi-elliptic interpolation, the divergencefree interpolation problem is converted to a generalized Stokes problem. To numerically solve this new problem, an Uzawa-type method and the method of fundamental solutions are proposed. In the second method, a linear system with large and dense matrix is to be solved, while in the first method, this problem is avoided.

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Acknowledgement

The research was partly supported by the European Union (co-financed by the European Regional Development Fund) under the project TÁMOP-4.2.2-08/1-2008-0021.

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Authors and Affiliations

  1. Széchenyi István University, P.O.Box 701, H-9007, Györ, Hungary

    Csaba Gáspár

Authors
  1. Csaba Gáspár
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Correspondence to Csaba Gáspár .

Editor information

Editors and Affiliations

  1. Inst. Numerische Simulation, Universität Bonn, Wegelerstr. 6, Bonn, 53115, Germany

    Michael Griebel

  2. Inst. f. Parallele und Verteilte Systeme, Universität Stuttgart, Universitätsstr. 38, Stuttgart, 70569, Germany

    Marc Alexander Schweitzer

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Gáspár, C. (2011). Meshfree Vectorial Interpolation Based on the Generalized Stokes Problem. In: Griebel, M., Schweitzer, M. (eds) Meshfree Methods for Partial Differential Equations V. Lecture Notes in Computational Science and Engineering, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16229-9_4

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