Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains
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 & 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 unfitted 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 -norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.
Keywords
Cite
@article{arxiv.1910.03054,
title = {Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains},
author = {Erik Burman and Stefan Frei and Andre Massing},
journal= {arXiv preprint arXiv:1910.03054},
year = {2020}
}