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Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

Published online by Cambridge University Press:  03 June 2015

Ahmad Shirzadi  and
Leevan Ling
Ahmad Shirzadi*
Affiliation:
Department of Mathematics, Persian Gulf University, Bushehr, Iran
Leevan Ling*
Affiliation:
Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
*
Corresponding author. Email: shirzadi.a@gmail.com
Email: lling@hkbu.edu.hk
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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 step-functions. 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.

Keywords

35J2565N1265D30Local integral equationsmeshless methodsradial basis functionsoverdetermined systemssolvabilityconvergence
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 5 , Issue 1 , February 2013 , pp. 78 - 89
Copyright
Copyright © Global-Science Press 2013

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