中文摘要：

考虑反应扩散方程的混合有限元求解方法．对方程通过先在粗网格上求解非线性问题。再在细网格上求解相应的线性问题，获得了两个两层网格算法．

英文摘要：

In this paper, we consider the two algorithms of two - grid scheme for the approximation of reaction - diffusion equations using a mixed finite - element method. Firstly, we solve an non - linear problem on the coarse grid, then, we preform two Newton iterations on the fine, and we obtained the error estimates of two - grid methods. It is showed that coarse space can be extremely coarse and achieve asymptotically optimal approximation. As a result, solving such a large class of non - linear equation will not be much more difficult than solving one single linearized equation.