Volume 5, Issue 1
Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs

Ahmad Shirzadi & Leevan Ling

Adv. Appl. Math. Mech., 5 (2013), pp. 78-89.

Published online: 2013-05

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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

Local integral equations meshless methods radial basis functions overdetermined systems solvability convergence

  • AMS Subject Headings

35J25 65N12 65D30

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COPYRIGHT: © Global Science Press

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@Article{AAMM-5-78, author = {Ahmad Shirzadi and Leevan Ling}, title = {Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2013}, volume = {5}, number = {1}, pages = {78--89}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.11-m11168}, url = {http://global-sci.org/intro/article_detail/aamm/58.html} }
TY - JOUR T1 - Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs AU - Ahmad Shirzadi & Leevan Ling JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 78 EP - 89 PY - 2013 DA - 2013/05 SN - 5 DO - http://doi.org/10.4208/aamm.11-m11168 UR - https://global-sci.org/intro/article_detail/aamm/58.html KW - Local integral equations KW - meshless methods KW - radial basis functions KW - overdetermined systems KW - solvability KW - convergence AB -

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.

Ahmad Shirzadi & Leevan Ling. (1970). Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs. Advances in Applied Mathematics and Mechanics. 5 (1). 78-89. doi:10.4208/aamm.11-m11168
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