The paper is concerned with a mathematical for some chemical reaction which take place in ground water. The model can be decribed by the following initial boundary value problem (P) of the semilinear reaction-diffusion system: Where RN is a bounded domain, the boundary are is properly smooth, J= (0, T], di>0(i=1, 2, 3) are constants. i,j,m,r are positive integers, u,v,w are unkown functions, are given initial functions. Galerkin approximating scheme of (P) is deduced by making use of the finite element method. Besides, the analysis of the conveyance for the approximating solution and the optimal error estimates in L2 are demonstrated by taking advantage of the priori estimate theory and technique of differential equation.
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