| Issue |
ESAIM: M2AN
Volume 49, Number 5, September-October 2015
|
|
|---|---|---|
| Page(s) | 1429 - 1450 | |
| DOI | https://doi.org/10.1051/m2an/2015019 | |
| 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
Berlin,
Germany.
This email address is being protected from spambots. You need JavaScript enabled to view it.
2 Technische Universität Dresden,
Institut für Numerische Mathematik, 01062
Dresden,
Germany.
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Received:
1
August
2014
Revised:
25
March
2015
Abstract
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
This research work was partially supported by the German research foundation (DFG) under the Grant MA 4713/2-1.
© EDP Sciences, SMAI 2015
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