On discontinuous Galerkin methods

Discontinuous Galerkin methods have received considerable attention in recent years for problems in which advection and di usion terms are present. Several alternatives for treating the di usion and advective uxes have been introduced. This report summarizes some of the methods that have been proposed. Several numerical examples are included in the paper. These present discontinuous Galerkin solutions of one-dimensional problems with a scalar variable. Results are presented for di usion–reaction problems and advection–di usion problems. We discuss the performance of various formulations with respect to accuracy as well as stability of the method