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

Abstract 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.