Local Heaviside weighted MLPG meshless method approach to extended Flamant problem using radial basis functions

The meshless local Petrov-Galerkin (MLPG) method with Heaviside step function as the weighting function is applied to solve the extended Flamant problem. There are two different classes of trial functions considered in the paper: classical radial basis functions (RBF) as extended multiquadrics and compactly supported radial basis functions (CSRBF) as Wu and Wendland functions. The method presented is a truly meshless method based on a set of nodes only. This approach allows direct imposing of essential boundary conditions; moreover, no domain integration is needed and no stiffness matrix assembly is required. The solution of the extended Flamant problem is presented. The performance of RBFs and CSRBFs proposed is compared and the effect of the sizes of local subdomain and interpolation domain is studied. The results obtained show the accuracy and numerical performance of the method.