On modified Gordon-Wixom interpolation schemes and their applications to nonlinear and exterior domain problems

Alexander Belyaev, Pierre-Alain Fayolle

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Abstract

We introduce and study extensions and modifications of the Gordon-Wixom transfinite barycentric interpolation scheme (Gordon and Wixom, SIAM J. Numer. Anal. 11(5), 909–933, 1974). We demonstrate that the modified Gordon-Wixom scheme proposed in Belyaev and Fayolle (Comput. Graph. 51, 74–80, 2015) reproduces harmonic quadratic polynomials in convex domains. We adapt the scheme for dealing with the exterior of a bounded domain and for the exterior of a disk, where we demonstrate that our interpolation formula reproduces harmonic functions. Finally, we show how to adapt the Gordon-Wixom approach for approximating p-harmonic functions and to derive computationally efficient approximations of the solutions to boundary value problems involving the p-Laplacian.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalNumerical Algorithms
Early online date27 May 2017
DOIs
Publication statusE-pub ahead of print - 27 May 2017

Keywords

  • Gordon-Wixom interpolation
  • Mean-value coordinates
  • p-Laplacian
  • Pseudo-harmonic interpolation.
  • Transfinite barycentric coordinates

ASJC Scopus subject areas

  • Applied Mathematics

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