Burman, E;
Ern, A;
Fernández, MA;
(2017)
Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem.
ESAIM: Mathematical Modelling and Numerical Analysis
, 51
(2)
pp. 487-507.
10.1051/m2an/2016028.
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Abstract
This paper deals with the spatial and time discretization of the transient Oseen equations. Finite elements with symmetric stabilization in space are combined with several time-stepping schemes (monolithic and fractional-step). Quasi-optimal (in space) and optimal (in time) error estimates are established for smooth solutions in all flow regimes. We first analyze monolithic time discretizations using the Backward Differentation Formulas of order 1 and 2 (BDF1 and BDF2). We derive a new estimate on the time-average of the pressure error featuring the same robustness with respect to the Reynolds number as the velocity estimate. Then, we analyze fractional-step pressure-projection methods using BDF1. The stabilization of velocities and pressures can be treated either implicitly or explicitly. Numerical results illustrate the main theoretical findings.
| Type: | Article |
|---|---|
| Title: | Fractional-step methods and finite elements with symmetric stabilization for the transient Oseen problem |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1051/m2an/2016028 |
| Publisher version: | http://doi.org/10.1051/m2an/2016028 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Oseen equations, stabilized finite elements, fractional-step methods, pressure-correction methods, error estimates, high Reynolds number |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1546108 |
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