Meshless Local Petrov-Galerkin (MLPG) Method for Convection-Diffusion Problems
H. Lin, S.N. Atluri

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 1, No. 2, pp. 45-60, 2000
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Keywords MLPG, MLS, convection-dominated flow, upwinding
Abstract Due to the very general nature of the Meshless Local Petrov-Galerkin (MLPG) method, it is very easy and natural to introduce the upwinding concept (even in multi-dimensional cases) in the MLPG method, in order to deal with convection-dominated flows. In this paper, several upwinding schemes are proposed, and applied to solve steady convection-diffusion problems, in one and two dimensions. Even for very high Peclet number flows, the MLPG method, with upwinding, gives very good results. It shows that the MLPG method is very promising to solve the convection-dominated flow problems, and fluid mechanics problems.
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