Numerical study of SUPG and LPS methods combined with higher order variational time discretization schemes applied to time-dependent convection-diffusion-reaction equations
- Ahmed, Naveed
- Matthies, Gunar
2010 Mathematics Subject Classification
- 65M12 65M15 65M60
- stabilized finite elements, discontinuous Galerkin, continuous Galerkin--Petrov, transient convection-diffusion-reaction equations
This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamline-upwind Petrov-Galerkin (SUPG) and local projection stabilization (LPS) methods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) methods and continuous Galerkin-Petrov (cGP) methods. Several numerical tests have been performed to assess the accuracy of combinations of spatial and temporal discretization schemes. Furthermore, the dependence of the results on the stabilization parameters of the spatial discretizations are discussed. Finally the long-time behavior of overshoots and undershoots is investigated.
- J. Sci. Comput., 67 (2016) pp. 988--1018.