Abstract
We present a scheme for solving two-dimensional semi-linear reaction–diffusion equations using an expanded mixed finite element method. To linearize the mixed-method equations, we use a two-grid scheme based on the Newton iteration method. We give the L p error estimate to the variable p in the two-grid solution. It is shown that the algorithm achieve asymptotically optimal approximation applying the two-grid methods as long as the mesh sizes satisfy H = O ( h 1 / 3 ) for semi-linear problems.
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