Meshless numerical method based on the local boundary integral equation (LBIE) to solve linear and non-linear boundary value problems

Tulong Zhu, Jindong Zhang, S. N. Atluri

Research output: Contribution to journalArticle

112 Scopus citations

Abstract

A meshless method for solving linear and non-linear boundary value problems is described. Numerical examples are given for several linear and non-linear problems, for which exact solutions are available. The described method converges fast to the final solution with reasonably accurate results for both the unknown variable and its derivatives in solving non-linear problems. The numerical results in these examples show that high rates of convergence with mesh refinement for the Sobolev norms ∥·∥0 and ∥·∥1 are achievable, and that the values of the unknown variable and its derivatives are accurate.

Original languageEnglish
Pages (from-to)375-389
Number of pages15
JournalEngineering Analysis with Boundary Elements
Volume23
Issue number5
DOIs
StatePublished - 1999

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