LpLp error estimates of two-grid schemes of expanded mixed finite element methods

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 LpLp 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(h1/3)H=O(h1/3) for semi-linear problems.