WIAS Preprint No. 1990, (2014)

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


  • Ahmed, Naveed
    ORCID: 0000-0002-9322-0373
  • 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.

Appeared in

  • ESAIM Math. Model. Numer. Anal., 49 (2015) pp. 1429--1450.

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