Discontinuous Petrov-Galerkin (DPG) methods for convection-diffusion problems

We discuss Petrov-Galerkin discretizations with optimal test spaces, or equivalently, least squares methods, for solving convection-dominated convection diffusion problems. In view of the expected occurrence of layers, we aim at methods that yield near-best approximations for the primal field variable in L2 by discontinuous piecewise polynomials. A necessary condition for obtaining a robust method is that it still applies in the limit of a vanishing diffusion. We compare some existing and new PG formulations in view of both these design principles, and illustrate our findings with some numerical comparisons.

The talk is based on joint work with Dirk Broersen (KdVI, Amsterdam).