A two-grid method for mixed finite-element solution of reaction-diffusion equations

Abstract

We present a scheme for solving two-dimensional, nonlinear reaction-diffusion equations, using a mixed finite-element method. To linearize the mixed-method equations, we use a two grid scheme that relegates all the Newton-like iterations to a grid ΔH much coarser than the original one Δh, with no loss in order of accuracy so long as the mesh sizes obey . The use of a multigrid-based solver for the indefinite linear systems that arise at each coarse-grid iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 317–332, 1999