Convergence analysis of a hierarchical enrichment of Dirichlet boundary conditions in a mesh-free method

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18 Scopus citations

Abstract

Implementation of Dirichlet boundary conditions in mesh-free methods is problematic. In Wagner and Liu (International Journal for Numerical Methods in Engineering 2001; 50:507), a hierarchical enrichment technique is introduced that allows a simple implementation of the Dirichlet boundary conditions. In this paper, we provide some error analysis for the hierarchical enrichment mesh-free technique. We derive optimal order error estimates for the hierarchical enrichment mesh-free interpolants. For one-dimensional elliptic boundary value problems, we can directly apply the interpolation error estimates to obtain error estimates for the mesh-free solutions. For higher-dimensional problems, derivation of error estimates for the mesh-free solutions depends on the availability of an inverse inequality. Numerical examples in ID and 2D are included showing the convergence behaviour of mesh-free interpolants and mesh-free solutions when the hierarchical enrichment mesh-free technique is employed.

Original languageEnglish (US)
Pages (from-to)1323-1336
Number of pages14
JournalInternational Journal for Numerical Methods in Engineering
Volume53
Issue number6
DOIs
StatePublished - Feb 28 2002

Keywords

  • Dirichet boundary condition
  • Error estimate
  • Hierarchical enrichment mesh-free technique
  • Mesh-free method

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics

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