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

Ahmed, Naveed; Matthies, Gunar

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

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.

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

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