Two-Grid Method For Mixed Finite-Element Solution Of Reaction-Diffusion Equations

In this paper, we give one kind of mixed Finite element method to solve the Reaction-diffusion equationsIn order to get down the size of the discrete system, we use the two-grid method. It solve a non-linear system on the coarse gridâ–³_H, then a linear system on the fine gridâ–³_h(H >> h). When the degree of the approximate space Raviart - thomas space k vanishes, using the existent two-grid method we can get just the same error estimates as the one which we solve a non-linear system on the fine grid so long as H = O(h^1/2) .The method we give in this paper use a recovery operator on the solution of the coarse grid, which release the requirement of H to H = O(h^1/3) when k = 0.