Analysis of the discontinuous Galerkin method for nonlinear convection–diffusion problems

Abstract

The subject-matter is the analysis of the discontinuous Galerkin finite element method applied to a nonlinear convection–diffusion problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. This allows us to consider general polyhedral elements with mutually disjoint interiors. We do not require their convexity, but assume only that they are star-shaped. We present an error analysis for the case of a nonsymmetric discretization of diffusion terms. Theoretical results are accompanied by numerical experiments.