Browsing by Author "Dallmann, Helene"

We consider conforming finite element (FE) approximations of the time-dependent, incompressible Navier-Stokes problem with inf-sup stable approximation of velocity and pressure. In case of high Reynolds numbers, a local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence-free constraint. For the arising nonlinear semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies and Tobiska (IMA J. Numer. Anal., to appear) for the linearized model and takes partly advantage of the analysis in Burman and Fernandez, Numer. Math. 107 (2007), 39-77 for edge-stabilized FE approximation of the Navier-Stokes problem. Some numerical experiments complement the theoretical results. (c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1224-1250, 2015

We consider conforming finite element approximations of the time-dependent Oseen problem with infsup stable approximation of velocity and pressure. The work serves as a preliminary study of the incompressible Navier-Stokes problem. In the case of high Reynolds numbers, the local projection stabilization method is considered. In particular, the idea of streamline upwinding is combined with stabilization of the divergence-free constraint. For the arising semidiscrete problem, a stability and convergence analysis is given. Our approach improves some results of a recent paper by Matthies & Tobiska (2014, IMA J. Numer. Anal., 35, 239-269). Finally, we apply the approach to the time-dependent incompressible Navier-Stokes problem, test the accuracy of the method and conduct numerical experiments with simple boundary layers and separation.

We consider conforming finite element approximations for the time-dependent Oberbeck-Boussinesq model with inf-sup stable pairs for velocity and pressure and use a stabilization of the incompressibility constraint. In case of dominant convection, a local projection stabilization method in streamline direction is considered both for velocity and temperature. For the arising nonlinear semi-discrete problem, a stability and convergence analysis is given that does not rely on a mesh width restriction. Numerical experiments validate a suitable parameter choice within the bounds of the theoretical results.