Discontinuous Galerkin method of lines for solving nonstationary singularly perturbed linear problems

• Published in: Journal of numerical mathematics Vol. 12; no. 2; pp. 97 - 117
• Main Authors: Feistauer, M., Švadlenka, K.
• Format: Journal Article
• Language: English
• Published: Genthiner Strasse 13 10875 Berlin Germany Walter de Gruyter 01.06.2004
• Subjects: asymptotic error estimates; discontinuous Galerkin finite element method; interior and boundary penalty; linear nonstationary convection–diffusion–reaction equation; nonsymmetric stabilization of diffusive terms; numerical experiments; upwinding
• ISSN: 1570-2820; 1569-3953
• DOI: 10.1515/156939504323074504

The subject-matter is the analysis of the discontinuous Galerkin finite element method of lines applied to a linear nonstationary convection–diffusion–reaction problem. In the contrary to the standard FEM the requirement of the conforming properties is omitted. The discretization is carried out with respect to space variables, whereas time remains continuous. In the discontinuous Galerkin discretization, the nonsymmetric stabilization of diffusion terms combined with interior and boundary penalty is applied. In the evaluation of fluxes the idea of upwinding is used. This allows to obtain an optimal error estimate, also verified by numerical experiments.