Burman, E;
Frei, S;
Massing, A;
(2022)
Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains.
Numerische Mathematik
10.1007/s00211-021-01264-x.
(In press).
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Abstract
This article is concerned with the discretisation of the Stokes equations on time- dependent domains in an Eulerian coordinate framework. Our work can be seen as an extension of a recent paper by Lehrenfeld and Olshanskii (ESAIM: M2AN 53(2):585–614, 2019), where BDF-type time-stepping schemes are studied for a parabolic equation on moving domains. For space discretisation, a geometrically unfit- ted finite element discretisation is applied in combination with Nitsche’s method to impose boundary conditions. Physically undefined values of the solution at previous time-steps are extended implicitly by means of so-called ghost penalty stabilisations. We derive a complete a priori error analysis of the discretisation error in space and time, including optimal L2(L2)-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.
| Type: | Article |
|---|---|
| Title: | Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s00211-021-01264-x |
| Publisher version: | https://doi.org/10.1007/s00211-021-01264-x |
| Language: | English |
| Additional information: | This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. |
| 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-pp.ucl.ac.uk/id/eprint/10142146 |
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