Error Estimate of the DGFEM for Nonlinear Convection-Diffusion Problems

This paper is concerned with the analysis of the full discrete discon-tinuous Galerkin finite element method (DGFEM) applied to the space full-discretization of non-linear nonstationary convection-diffusion prob-lem with nonlinear convection in two dimensions. General nonconform-ing simplicity meshes are considered and symmetric interior penalty Galerkin (SIPG)scheme is used. The error analysis is carried out for nonconforming triangular meshes. we prove the approximate solution is converges with error of order (h2 + 2)