Nonstandard Meshless Local Petrov-galerkin Method for Solving Convection Diffusion Equation

Numerical solutions to the stationary convection diffusion problems with dominant convective term by the meshless local Petrov-Galerkin method are corrupted by spurious oscillations.In this paper,based on the ideas of the Streamline Upwind Petrov-Galerkin method and the Galerkin Least-Squares method,two nonstandard meshless local Petrov-Galerkin methods are developed to solve the stationary convection diffusion problems with dominant convective term in two dimensions.The two methods avoid the numerical spurious oscillations when the convective term is dominant.Numerical examples are presented to illustrate feasibility and efficiency of the two methods.