An optimal L∞(L2)-error estimate for the discontinuous Galerkin approximation of a nonlinear non-stationary convection–diffusion problem

This paper is concerned with the analysis of the discontinuous Galerkin finite-element method applied to the space semi-discretization of a nonlinear non-stationary convection-diffusion problem. Attention is paid on the derivation of an L ∞ (L 2 )-optimal error estimate for the symmetric interior penalty Galerkin scheme. The error analysis is performed for standard simplicial meshes under the assumption that the exact solution of the problem and the solution of an elliptic dual problem are sufficiently regular. The theoretical results are illustrated by numerical experiments.