Error Estimates of the Discontinuous Galerkin Method for Nonlinear Nonstationary Convection-Diffusion Problems

Abstract This paper is concerned with the analysis of the discontinuous Galerkin finite element method applied to the space semidiscretization of nonlinear nonstationary convection-diffusion problems. The attention is paid to the derivation of the method and the investigation of error estimates for schemes with a symmetric as well as nonsymmetric discretization of diffusion terms and with the interior and boundary penalty. The theoretical results are illustrated by numerical experiments.

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