Optimal error estimates in the DG method for nonlinear convection-diffusion problems

Abstract

The subject of the paper is the derivation of optimal error estimates for the discontiuous Galerkin space semi-discretization of a convection-diffusion problem with nonlinear convection and diffusion. The analysis is based on a nonlinear variant of the Aubin-Nitsche technique, which uses a linearized dual problem.

Handling the nonlinearity requires several important assumptions, such as a high regularity of the exact solution, convexity of the domain and the use of only Dirichlet boundary conditions.

Keywords

• Optimal
• error
• estimates
• method
• nonlinear
• convection-diffusion
• problems