Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations

Ahmed, Naveed; Matthies, Gunar

doi:10.1051/m2an/2015019

Ahmed, Naveed ¹ ; Matthies, Gunar ²

¹ Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117 Berlin, Germany.
² Technische Universität Dresden, Institut für Numerische Mathematik, 01062 Dresden, Germany.

ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1429-1450.

Résumé

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.

Reçu le : 2014-08-01

MR Zbl

DOI : 10.1051/m2an/2015019

Classification : 65M12, 65M15, 65M60
Mots-clés : Transient convection-diffusion-reaction problem, local projection stabilization, continuous Galerkin−Petrov method, discontinuous Galerkin method

Affiliations des auteurs :

Ahmed, Naveed ¹ ; Matthies, Gunar ²

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     title = {Higher order continuous {Galerkin\ensuremath{-}Petrov} time stepping schemes for transient convection-diffusion-reaction equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1429--1450},
     publisher = {EDP-Sciences},
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     year = {2015},
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Ahmed, Naveed; Matthies, Gunar. Higher order continuous Galerkin−Petrov time stepping schemes for transient convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 5, pp. 1429-1450. doi : 10.1051/m2an/2015019. http://www.numdam.org/articles/10.1051/m2an/2015019/

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