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Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains

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BURMAN, Erik, Stefan FREI, Andre MASSING, 2022. Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains. In: Numerische Mathematik. Springer. 150, pp. 423-478. ISSN 0029-599X. eISSN 0945-3245. Available under: doi: 10.1007/s00211-021-01264-x

@article{Burman2022Euler-55629.2, title={Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains}, year={2022}, doi={10.1007/s00211-021-01264-x}, volume={150}, issn={0029-599X}, journal={Numerische Mathematik}, pages={423--478}, author={Burman, Erik and Frei, Stefan and Massing, Andre} }

2022-01-26T08:59:55Z terms-of-use Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains Massing, Andre Burman, Erik 2022-01-26T08:59:55Z Frei, Stefan eng 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 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 L<sup>2</sup>(L<sup>2</sup>)-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples. Frei, Stefan Massing, Andre Burman, Erik 2022

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