A two-grid method for the semi-linear reaction-diffusion system of the solutes in the groundwater flow by finite volume element

Based on two different spaces defined on one coarse grid with mesh size H and one fine grid with mesh size h, a two-grid finite volume method is introduced to obtain the solutions of semi-linear reaction-diffusion equations of the solutes in the groundwater flow. The standard finite element Ritz projection and elliptic projection are applied to the analysis of this approach. Error estimates in L2 norm and H1 norm are derived in this paper. The above estimates can be applied to choose H=O(h1/4) in the H1 norm and H=O(h1/2) in the L2 norm for the coarse grid problems. Some numerical examples are presented to justify the efficiency and accuracy of the method.