摘要：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.
