Local RBF method for multi-dimensional partial differential equations.

In this paper, a local meshless differential quadrature collocation method is utilized to solve multi-dimensional reaction–convection–diffusion PDEs numerically. In some cases, global version of the meshless method is considered as well. The meshless methods approximate solution on scattered and uniform nodes in both local and global sense. In the case of convection-dominated PDEs, the local meshless method is coupled with an upwind technique to avoid spurious oscillations. For this purpose, a physically motivated local domain is utilized in the flow direction. Both regular and irregular geometries are taken into consideration. Numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains.