The finite element method solution of variable diffusion coefficient convection-diffusion equations

Mathematical modeling of many physical and engineering problems is defined with convection-diffusion equation. Therefore, there are many analytic and numeric studies about convection-diffusion equation in literature. The finite element method is the most preferred numerical method in these studies since it can be applied to many problems easily. But, most of the studies in literature are about constant coefficient case of the convection-diffusion equation. In the first part of this study, the finite element formulations of the constant coefficient case of the convection-diffusion equation are given in both one and two dimensional cases. Then, obtained formulations are generalized for variable diffusion coefficient equations. Finally, obtained formulations are tested on some problems in one and two dimensions and results are discussed.