Numerical Solutions forTwo-Dimensional Laplace Equation in Electrostatics with Boundary Values

Abstract

In this paper, numerical method algorithmsare designed and implemented for the solution of partial differential two dimensional Laplaceequations.Finite difference method (FDM)and Finite element method (FEM) approaches are used to determine the solution and the performance is investigated by developing algorithms in MATLAB. The electric potential over the entire domain for both methods are computed. The solution obtained using FEM is compared with FDM. In this problem, theFDM results are considered to bemore accurate. The accuracyof FEM solution can be increasedusing higher order elements or by dividing the given domain into a greater number of triangular elements.