OPTIMAL ERROR ESTIMATES IN THE DG METHOD FOR NONLINEAR CONVECTION-DIFFUSION PROBLEMS

This paper is concerned with the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonstationary convection-diffusion problem with nonlinear convection and nonlinear diffusion. Optimal estimates in the L(infinity)(L(2))-norm are derived for the symmetric interior penalty (SIPG) scheme in two dimensions. The error analysis is carried out for nonconforming triangular meshes under the assumption that the exact solution of the problem and the solution of a linearised elliptic dual problem are sufficiently regular.