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 L-2 and L-p-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 1 algorithms is analyzed, and the asymptotically optimal approximation is achieved with the relation H = O(h(1/2)). Finally, numerical examples are provided to confirm theoretical results.