Numerical Process Of Two Dimensional Laplace’s Equation Using Finite Difference and Finite Element Method
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Finite Difference Method, Finite Element Method, Two-Dimensional Laplace Equation
Abstract
This paper presents a study of the finite difference method and the finite element method to solve the problem of spreading of temperature in a thin metal square plate installed from the left side and the lower side on the coordinate axes and at zero centigrade, while the right and upper sides were kept at certain temperatures, which the two dimensional Laplace equation simulated with Dirichlet boundary conditions. In additions by using iterative methods as Jacobi method and Gauss- Seidel method to solve the system of linear algebraic equations. The study has showed that the numerical results of the finite difference method were identical with the numerical results of the finite element method and the two methods were highly accurate in comparison to the analytical solution. On the other hand, the method of Gauss- Seidel iterative was faster in solving linear equation systems and more accurate than Jacobi iterative method.
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