Gedif, Tsegaye (PhD)Kefyalew, Erimyas2018-07-132023-11-042018-07-132023-11-042016-07-12http://etd.aau.edu.et/handle/123456789/8399Elliptic partial dierential equations appear frequently in various elds of science and engineering. These involve equilibrium problems and steady state phenomena. The most common example of such equation is poisson's equation. Most of these physical problems are very hard to solve analytically, instead, they can be solved numerically using computational methods. The nite element method is the most popular numerical method for solving elliptic boundary value problems. In this project, we introduce the concept of weak formulation, the nite element method, the nite element interpolation theory and its application in error estimates of nite element solutions of linear elliptic boundary value problems. This project also include the numerical solution of a two dimensional poisson equation with dirichlet boundary conditions by nite element method. Keywords: Weak formulation, Finite Element Method, Poisson EquationenWeak formulationFinite Element MethodPoisson EquationThesis