Numerical solution of the advection diffusion equation by using finite element method

This study is constructed five chapters.In chapter one, some fundamental definitions are given.In chapter two, essential construction the Homotopy Perturbation Method, Adomian Decomposition Method and Galerkin Method are given.In chapter three, With initial conditions are given of Advection Diffusion Equation Galerkin Method, Homotopy Perturbation Method and Adomian Decomposition Method was applied to find approximate solutions. We drawn graphics (2D and 3D) of approximate solutions and exact solution which are obtained for equations.In chapter four, it is made conversation of obtained databases.In chapter five, it is suggested to apply Galerkin Method, Homotopy Perturbation Method and Adomian Decomposition Method to some linear or nonlinear differential equations by depending on obtained solutions.