| Abstract: | In this paper, we study an efficient scheme for nonlinear reaction-diffusion
equations discretized by mixed finite element methods. We mainly concern the case
when pressure coefficients and source terms are nonlinear. To linearize the nonlinear
mixed equations, we use the two-grid algorithm. We first solve the nonlinear equations
on the coarse grid, then, on the fine mesh, we solve a linearized problem using
Newton iteration once. It is shown that the algorithm can achieve asymptotically optimal
approximation as long as the mesh sizes satisfy $H =\mathcal{O}(h^{\frac{1}{2}})$. As a result, solving
such a large class of nonlinear equations will not be much more difficult than getting
solutions of one linearized system. |
