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 language | English (US) |
---|---|
Pages (from-to) | 1117-1126 |
Number of pages | 10 |
Journal | Engineering Analysis with Boundary Elements |
Volume | 37 |
Issue number | 7-8 |
DOIs | |
State | Published - Jul 2013 |
Bibliographical note
KAUST Repository Item: Exported on 2020-10-01ASJC Scopus subject areas
- Computational Mathematics
- Analysis
- Applied Mathematics
- General Engineering