Abstract
It is well known that convection-diffusion equations suffer from the most difficult problems to gain a stable and accurate solution. Sometimes, the convection terms may cause oscillatory behavior of solutions. In this article, the streamline upwind Petrov-Galerkin (SUPG) scheme is applied to eliminate overshoots and undershoots produced by the convection term in the meshless local Petrov-Galerkin (MLPG) method. The accuracy and stability of the present method are discussed using two test cases. The results of the present method are compared with results of other upwind schemes and the finite volume method (FVM) using a high-order upwind scheme. Our analysis shows that the present method, with its simple implementation, can give excellent results for convection-dominated problems.
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