Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs (Advances in Applied Mathematics and Mechanics, 2018)
This paper deals with the solvability and the convergence of a class ofunsymmetric Meshless Local Petrov-Galerkin (MLPG) method with radialbasis function (RBF) kernels generated trial spaces. Local weak-formtestings are done with step-functions. It is proved thatsubject to sufficiently many appropriate testings, solvability of theunsymmetric RBF-MLPG resultant systems can be guaranteed.Moreover, an error analysis shows that this numerical approximationconverges at the same rate as found in RBF interpolation.Numerical results (in double precision) give good agreement withthe provided theory.