Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equations Original Research Article

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