Numerical Analysis of a Finite Volume-element Method for Unsteady Diffusion-reaction Equation

Abstract

The paper presents the numerical analysis of a finite volume-element method for solving the unsteady scalar reaction-diffusion equations. The main idea of the method is to combine the concepts that are employed in the finite volume and the finite element method together. The finite volume method is used to discretize the unsteady reaction-diffusion equation, while the finite element method is applied to estimate the gradient quantities at cell faces. Robustness and efficiency of the combined method have been evaluated on uniform rectangular grids by using available numerical solutions of the two-dimensional reaction-diffusion problems. By implementing one-dimensional analysis, it is showed that the stability of the numerical scheme is given by the condition , and the scheme is consistent with an order of accuracy of with respect to norm.