Two-Grid Methods for Mixed Finite-Element Solution of Coupled Reaction-Di usion Systems

We develop two-grid schemes for solving nonlinear reaction-diiusion systems , @p @t ? r (Krp) = f(x; p); where p = (p; q) is an unknown vector-valued function. The schemes use discretizations based on a mixed nite-element method. The two-grid approach yields iterative procedures for solving the nonlinear discrete equations. The idea is to relegate all of the Newton-like iterations to grids much coarser than the nal one, with no loss in order of accuracy. The iterative algorithms examined here extend a method developed earlier for single reaction-diiusion equations. An application to pre-pattern formation in mathematical biology illustrates the method's eeectiveness.