Journal article
Convergence analysis of a hierarchical enrichment of Dirichlet boundary conditions in a mesh‐free method
International Journal for Numerical Methods in Engineering, Vol.53(6), pp.1323-1336
02/28/2002
DOI: 10.1002/nme.336
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 1D 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. Copyright © 2001 John Wiley & Sons, Ltd.
Details
- Title: Subtitle
- Convergence analysis of a hierarchical enrichment of Dirichlet boundary conditions in a mesh‐free method
- Creators
- Weimin HanGregory J WagnerWing Kam Liu - Northwestern University
- Resource Type
- Journal article
- Publication Details
- International Journal for Numerical Methods in Engineering, Vol.53(6), pp.1323-1336
- Publisher
- John Wiley & Sons, Ltd; Chichester, UK
- DOI
- 10.1002/nme.336
- ISSN
- 0029-5981
- eISSN
- 1097-0207
- Number of pages
- 14
- Grant note
- NSF ARO
- Language
- English
- Date published
- 02/28/2002
- Academic Unit
- Mathematics
- Record Identifier
- 9983985826402771
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