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Solvability of partial differential equations by meshless kernel methods

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Abstract

This paper first provides a common framework for partial differential equation problems in both strong and weak form by rewriting them as generalized interpolation problems. Then it is proven that any well-posed linear problem in strong or weak form can be solved by certain meshless kernel methods to any prescribed accuracy.

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong

    Y. C. Hon

  2. Institut für Numerische und Angewandte Mathematik, Lotzestraße 16–18, D37083, Göttingen, Germany

    Robert Schaback

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  1. Y. C. Hon
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  2. Robert Schaback
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Correspondence to Y. C. Hon.

Additional information

The work described in this paper was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 101205). Robert Schaback’s research in Hong Kong was sponsored by DFG and City University of Hong Kong.

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Hon, Y.C., Schaback, R. Solvability of partial differential equations by meshless kernel methods. Adv Comput Math 28, 283–299 (2008). https://doi.org/10.1007/s10444-006-9023-2

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  • DOI: https://doi.org/10.1007/s10444-006-9023-2

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