Higher order continuous Galerkin--Petrov time stepping schemes for transient convection-diffusion-reaction equations
- Ahmed, Naveed
- Matties, Gunar
2010 Mathematics Subject Classification
- 65M12 65M15 65M60
- transient convection-diffusion-reaction problem, local projection stabilization, continuous Galerkin--Petrov method, discontinuous Galerkin method
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.
- ESAIM Math. Model. Numer. Anal., 49 (2015) pp. 1429--1450.