Balázsová, Monika; Feistauer, Miloslav; Hadrava, Martin; Kosík, Adam On the stability of the space-time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection-diffusion problems. (English) Zbl 1327.65168 J. Numer. Math. 23, No. 3, 211-233 (2015). Summary: The subject of this paper is the analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme, the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty are used. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. An important tool is the concept of the discrete characteristic function. Theoretical results are accompanied by numerical experiments. Cited in 6 Documents MSC: 65M12 Stability and convergence of numerical methods 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 Keywords:nonlinear convection-diffusion problems; space-time discontinuous Galerkin method; space and time discretization; stability of the method; discrete characteristic function PDFBibTeX XMLCite \textit{M. Balázsová} et al., J. Numer. Math. 23, No. 3, 211--233 (2015; Zbl 1327.65168) Full Text: DOI