An implicit meshless scheme for the solution of transient non-linear Poisson-type equations

Georgios Bourantas, Vasilis N. Burganos

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Original languageEnglish (US)
Pages (from-to)1117-1126
Number of pages10
JournalEngineering Analysis with Boundary Elements
Volume37
Issue number7-8
DOIs
StatePublished - Jul 2013

ASJC Scopus subject areas

  • Computational Mathematics
  • Analysis
  • Applied Mathematics
  • Engineering(all)

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