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Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems

by Ahmed, N., Matthies, G., Tobiska, L., Xie, H..

Series: 2010-24, Preprints

65M12 Stability and convergence of numerical methods
65M15 Error bounds
65M60 Finite elements, ~Rayleigh-Ritz and Galerkin methods, finite methods

A time-dependent convection-diffusion-reactions problems is discretized in space by a continuous finite element method with local projection stabilization and in time by a discontinuous Galerkin method. We present error estimates for the semidiscrete problem after discretizing in space
only and for the fully discrete problem. Numerical tests confirm the theoretical results.

discontinuous Galerkin, stabilized finite elements, convection-diffusion-reaction equation