Volume 49, Number 5, September-October 2015
|Page(s)||1429 - 1450|
|Published online||02 September 2015|
Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations∗
1 Weierstrass Institute for Applied
Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117
2 Technische Universität Dresden, Institut für Numerische Mathematik, 01062 Dresden, Germany.
Revised: 25 March 2015
We present the analysis for the higher order continuous Galerkin−Petrov (cGP) time discretization schemes in combination with the one-level local projection stabilization in space applied to time-dependent convection-diffusion-reaction problems. Optimal a priori error estimates will be proved. Numerical studies support the theoretical results. Furthermore, a numerical comparison between continuous Galerkin−Petrov and discontinuous Galerkin time discretization schemes will be given.
Mathematics Subject Classification: 65M12 / 65M15 / 65M60
Key words: Transient convection-diffusion-reaction problem / local projection stabilization / continuous Galerkin−Petrov method / discontinuous Galerkin method
© EDP Sciences, SMAI 2015
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