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Article

Balázsová, Monika ; Feistauer, Miloslav ; Hadrava, Martin ; Kosík, Adam
Stability analysis of the space-time discontinuous Galerkin method for nonstationary nonlinear convection-diffusion problems. (English). In: Chleboun, J., Přikryl, P., Segeth, K., Šístek, J. and Vejchodský, T. (eds.): Programs and Algorithms of Numerical Mathematics. Proceedings of Seminar. Dolní Maxov, June 8-13, 2014. Institute of Mathematics AS CR, Prague, 2015. pp. 9-16
MSC: 65M12, 65M60
Keywords:
error estimates; unconditional stability; interior penalty; boundary penalty
Summary:
This paper is concerned with the stability analysis of the space-time discontinuous Galerkin method for the solution of nonstationary, nonlinear, convection-diffusion problems. In the formulation of the numerical scheme we use the nonsymmetric, symmetric and incomplete versions of the discretization of diffusion terms and interior and boundary penalty. Then error estimates are briefly characterized. The main attention is paid to the investigation of unconditional stability of the method. Theoretical results are demonstrated by a numerical example.
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