On the stability of the space–time discontinuous Galerkin method for the numerical solution of nonstationary nonlinear convection–diffusion problems

• Published in: Journal of numerical mathematics Vol. 23; no. 3; pp. 211 - 233
• Main Authors: Balázsová, Monika, Feistauer, Miloslav, Hadrava, Martin, Kosík, Adam
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.09.2015; Walter de Gruyter GmbH
• Subjects: Boundaries; Diffusion; discrete characteristic function; Discretization; Economic models; Galerkin methods; Mathematical analysis; Mathematical models; Nonlinear convection-diffusion problems; Nonlinearity; space and time discretization; space-time discontinuous Galerkin method; Stability; stability of the method
• ISSN: 1570-2820; 1569-3953
• DOI: 10.1515/jnma-2015-0014

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.