Numerical studies of variational-type time-discretization techniques for transient Oseen problem

Abstract

In this paper, we combine continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time stepping schemes with local projection method applied to inf-sup stable discretization of the transient Oseen problem. Using variational-type time-discretization methods of polynomial degree k, we show that the cGP(k) and dG(k) methods are accurate of order k+1, in the whole time interval. Moreover, in the discrete time points, the cGP(k)-method is super convergent of order 2k and the dG(k)-method is of order 2k +1. Furthermore, the dependence of the results on the choice of the stabilization parameters are discussed.