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

Abstract

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 multiqudrics and compactly supported radial basis functions (CSRBF) as Wu and Wendland functions. The presented method is a truly meshless method based only on a set of nodes. This approach allows for direct imposing of essential boundary conditions, moreover - no domain integration is needed and no stiffness matrix assembly is required. The solution of extended Flamant problem is presented. The performance of proposed RBFs and CSRBFs is compared and the effect of the sizes of local subdomain and interpolation domain is studied. Results show the accuracy and numerical performance of the method.