Mixed Finite-element Solution of Reaction-diiusion Equations Using a Two-grid Method

We present a method for solving nonlinear reaction-diiusion equations, s @p @t ? r (Krp) = f (p); using a mixed nite-element method. To linearize the mixed-method equations , we use a two-grid scheme that relegates all of the Newton-like iterations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indeenite linear systems that arise at each iteration, as well as for the similar system that arises on the ne grid, allows for even greater eeciency.