Eccentric LRPIM for Convection Dominated Problems

The purpose of this paper is mainly focused on the stability problem in the numerical analysis of the convection dominated problems. Due to the advantages of dealing with boundary conditions and introducing upwinding concept, an improved local radial point interpolation method (ELRPIM) is presented to deal with the convection dominated problems. Based on the local radial point interpolation method (LRPIM) and an eccentric test function, the ELRPIM has been proposed. Then the effect of ELRPIM is discussed through some examples in one-dimension. The results show that: both the LRPIM and ELRPIM are effective to resolve steady convection dominated problem when the Peclet number is low; along with the increase of the Peclet number, only the ELRPIM gives very good results; the optimal offset e that makes the numerical result error optimal increases with the increase of the Peclet number. It is thus concluded that the ELRPIM is very promising to solve the convection dominated problems.