GLOBAL DYNAMICS OF A DISCONTINUOUS GALERKIN APPROXIMATION TO A CLASS OF REACTION-DIFFUSION EQUATIONS

The long time behavior of arbitrary order fully discrete approximation s using the discontinuous Galerkin method (see Johnson, 1987) for the time discretization of a reaction-diffusion equation is studied. The e xistence of absorbing sets and an attractor is shown for the numerical method. The crucial step in the analysis involves showing the fully d iscrete scheme has a Lyapunov functional.