Department of Mathematics
Convergent overdetermined-RBF-MLPG for solving second order elliptic PDEs
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 stepfunctions. 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. © 2013 Global Science Press.
Convergence, Local integral equations, Meshless methods, Overdetermined systems, Radial basis functions, Solvability
Source Publication Title
Advances in Applied Mathematics and Mechanics
The Global Science Journal
Link to Publisher's Edition
Shirzadi, Ahmad, and Leevan Ling. "Convergent overdetermined-RBF-MLPG for solving second order elliptic PDEs." Advances in Applied Mathematics and Mechanics 5.1 (2012): 78-89.