Higher Order Compact Finite Difference Method And Finite Element Method For Solving 2d Poisson?�?s Equations

Abstract

The main purpose of this thesis is to solve the 2D Elliptic Boundary Value Problems using higher-order CFDM and FEM. We derived eight-order compact finite difference schemes to solve the 2D-Poisson equation subject to Dirichlet boundary condition on a bounded two dimensional region by using Taylor series expansion. In eight order compact finite difference for solving 2D-Poisson equations, the suggested scheme has the stencil of twenty five points. By using steps of finite element method in rectangu lar elements we obtained 9-point finite difference method in assembling elements. The numerical solutions were obtained by these two methods were compared with each other graphically in two dimension. Accuracy of the finite difference technique can be im proved by representing the partial differential equation by a higher order approximation developed to reduce the Taylor series truncation error. Therefore, eight-order compact finite difference schemes have higher accuracy than six-order compact finite difference schemes and finite element method for solving 2D Poisson equations.