FINITE DIFFERENCE METHOD ON TRIANGULATION

Abstract. In this paper, we present a new method for solving Partial Differential Equations (PDE). This method combines the use of features of both Finite Element Methods (FEM) and Finite Difference methods (FDM). Similar to the FEM, this method uses the triangulation technique and function approximation. Moreover, it uses direct discretization of the PDE, similar to the FDM. The basic idea starts by selecting a finite difference representation of the PDE and a triangular element. The selected representation involves nodal point and non-nodal points. Then, the selected triangular element is used to approximate the function values of the non-nodal points. This method can be seen as a finite difference method when an irregular nodal arrangement is appropriate for a given problem. Derivation of the method with remarks is presented as well as several computational examples with their graphs and tables