A New Two-Grid Mixed Finite Element Analysis of Semi-Linear Reaction-Diffusion Equation.

A new mixed finite element method is established for solving the semi-linear reaction–diffusion equation based on two-grid discretization. Here, a symmetric positive definite mixed finite element method is constructed for semi-linear problem, and the corresponding error estimates in L2 and Lp-norms are considered. Then, the two-grid techniques with and without one Newton iteration correction are applied for the proposed mixed element procedure to improve the efficiency of computation. The corresponding convergence of the proposed algorithms is analyzed, and the asymptotically optimal approximation is achieved with the relation H=O(h12). Finally, numerical examples are provided to confirm theoretical results.