Application Of Lopi Method To Convection Dominated Problems.

Abstract

The Local Optimal Point Interpolation (LOPI) method is a truly meshless
method based on the boolean sum of a radial basis function interpolator and a least
squares approximation in a polynomials space. In this way, it can interpolate solutions in
data points, while at the same time fit exactly polynomial solutions up to certain degree.
Systems of PDEs could be solved in strong form using point collocation, without meshes
or integration cells. In this work, we introduce the use of LOPI method in convection
dominated problems under an upwind scheme. As a main example, this scheme is applied
as a spatial approximation for solving the nonlinear Burger’s equation. For comparison
purposes, a low order explicit finite difference approximation of the time derivative is
employeed. Numerical comparisons are made with existing numerical schemes for solving
the Burger’s equation.