Analysis of the DGFEM for nonlinear convection-diffusion problems. (English) Zbl 1171.65070
Summary: The paper is concerned with the analysis of error estimates of the discontinuous Galerkin finite element method (DGFEM) for the numerical solution of nonstationary nonlinear convection-diffusion problems equipped with Dirichlet boundary conditions. First, the case of nonlinear diffusion as well as nonlinear convection is considered. Then, the optimal \(L^\infty(L^2)\)-error estimate is discussed in the case of nonlinear convection and linear diffusion.
MSC:
65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
35K55 | Nonlinear parabolic equations |