Numerical Solution for One- Dimensional Differential Equation Using the Finite Element Method

Abstract

The finite element method is presented in this thesis, and we applied it for obtaining the approximate solution to the two points boundary value problem. This method uses the Galerkin method and the variational (weak) formulation to convent the stronge form of the problem to linear algebriac system which we solved it by using Matlab program. We estimate the errors for the solution using linear and quadratic basis. We also show the equivelance relation between Galerkin method and the minimizing of the problems. We also showed the uniqueness of the solution using the finite element problem.