L ∞ (L 2)-error estimates for the DGFEM applied to convection–diffusion problems on nonconforming meshes

Abstract This paper is devoted to the analysis of the discontinuous Galerkin finite element method (DGFEM) applied to the space semidiscretization of a nonlinear nonstationary convection–diffusion Dirichlet problem. General nonconforming simplicial meshes are considered and the SIPG scheme is used. Under the assumption that the exact solution is sufficiently regular an L ∞ (L 2)-optimal error estimate is derived. The theoretical results are illustrated by numerical experiments.

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