CONVERGENCE ANALYSIS AND UPPER BOUND PROPERTY OF NS-RPIM WITH PURE RBFS USING VORONOI SMOOTHING DOMAINS

In this paper, a nodal based smoothed point interpolation method (NS-RPIM) is implemented using Voronoi smoothing domains to solve elliptic partial differential equations with different node selection strategies. Shape functions for field variable approximation are built using the radial point interpolation method (RPIM) with pure radial basis functions (RBFs) without polynomial basis. The smoothed Galerkin weak form is applied to construct the discretized system equations. Triangle background cells with voronio smoothing domains and quadrilateral mesh with smoothing domains of equally-shared areas are used. It is found that in all cases that the NS-RPIM provides results with higher convergency rates for distorted mesh compared with the standard FEM. In addition, in all numerical examples, solutions for the energy norm by NS-RPIM are found to be upper bounds with respect to the FEM counterparts and even to exact solutions. In terms of accuracy, however, NS-RPIM could be more or less accurate than that of FEM dependent on the problem.