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

摘要

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 L~2 norm and H~1 norm are derived in this paper. The above estimates can be applied to choose H = O(h~(1/4)) in the H~1 norm and H = O(h~(1/2)) in the L~2 norm for the coarse grid problems. Some numerical examples are presented to justify the efficiency and accuracy of the method.