Convergent overdetermined-RBF-MLPG for solving second order elliptic pdes

Ahmad Shirzadi*, Leevan LING

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

16 Citations (Scopus)

Abstract

This paper deals with the solvability and the convergence of a class of unsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radial basis function (RBF) kernels generated trial spaces. Local weak-form testings are done with stepfunctions. It is proved that subject to sufficiently many appropriate testings, solvability of the unsymmetric RBF-MLPG resultant systems can be guaranteed. Moreover, an error analysis shows that this numerical approximation converges at the same rate as found in RBF interpolation. Numerical results (in double precision) give good agreement with the provided theory.

Original languageEnglish
Pages (from-to)78-89
Number of pages12
JournalAdvances in Applied Mathematics and Mechanics
Volume5
Issue number1
DOIs
Publication statusPublished - 2013

Scopus Subject Areas

  • Mechanical Engineering
  • Applied Mathematics

User-Defined Keywords

  • Convergence
  • Local integral equations
  • Meshless methods
  • Overdetermined systems
  • Radial basis functions
  • Solvability

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