Solving Laplace Equations Using Finite Element Method

Abstract

In this thesis,FEM has been used to solve the 2D Laplace equations over regular domain.The FEM discritization involves both triangular and rectangular element. A simple test examples were given to check the applicability of FEM with various number of nodal points. The computational accuracy results are based on error analysis shown in tables and graphs.The study shows that increasing the number of nodes may increase accuracy. By using this method and analysis the result were given for three different examples. To show the effectiveness of this method with the help of mathlab program code. The result of the given examples were displayed using tables and graphs for numerical solution, exact solution and absolute error. From the result obtained compared the three results.The absolute error was ob tained by subtracting the numerical solution from analytic solution. As the number of node increases the error decreases and converges to exact solution.The graph of numerical solution and analytic solutions was nearly similar.This shows the effec tiveness, efficiency and reliability of using FEM of solving two dimensional Laplace equations