An optimal \(L^\infty(L^{2})\)-error estimate for the discontinuous Galerkin approximation of a nonlinear non-stationary convection-diffusion problem. (English) Zbl 1158.65067

Dolejší, Vít; Feistauer, Miloslav; Kučera, Václav; Sobotíková, Veronika

IMA J. Numer. Anal. 28, No. 3, 496-521 (2008).

The paper is devoted to the derivation of an \(L^{\infty}(L_2)\) optimal error estimate for a semi-discretization of a nonlinear, non-stationary convection-diffusion problem, where a discontinuous Galerkin approximation for the spatial operator is used. The main results are illustrated by numerical experiments.

Reviewer: Iwan Gawriljuk (Eisenach)

MSC:

65M20	Method of lines for initial value and initial-boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55	Nonlinear parabolic equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

non-stationary convection-diffusion problem; discontinuous Galerkin approximation; optimal \(L^{\infty}(L_2)\)-error estimate; finite-element method; interior and boundary penalty; method of lines; convergence; semi-discretization; numerical experiments