In this thesis, a finite volume element method for two-dimensional, unsteady-state convection-diffusion-reaction equation is presented. The corresponding finite volume element equation is derived from the partial differential equation which satisfy the convection-diffusion-reaction problem. To analyze the convection-diffusion-reaction problems, the triangular control volumes are used. Finite volume element computer program from finite volume element equation is developed and verified by solving the problems of which exact solutions and previous numerical results are available. To improve solution accuracy and save computational time, an adaptive meshing technique is applied to the finite volume element method. The technique places small control volumes in the region of high solution gradients, and vice versa. Results from the convection-diffusion-reaction problems assure the efficiency of applying the finite volume element method with adaptive meshing technique, which are proposed in this thesis.
