A numerical study of divergence-free kernel approximations

Arthur A. Mitrano, Rodrigo Platte

Research output: Contribution to journalArticle

Abstract

Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.

Original languageEnglish (US)
Pages (from-to)94-107
Number of pages14
JournalApplied Numerical Mathematics
Volume96
DOIs
StatePublished - May 30 2015

Keywords

  • Divergence-free
  • Finite-differences
  • Radial basis functions
  • Spectral methods

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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