Publikation: Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains
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2022
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Numerische Mathematik. Springer. 2022, 150, pp. 423-478. ISSN 0029-599X. eISSN 0945-3245. Available under: doi: 10.1007/s00211-021-01264-x
Zusammenfassung
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 L2(L2)-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.
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510 Mathematik
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undefined / . - undefined, undefined
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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. 2022, 150, pp. 423-478. ISSN 0029-599X. eISSN 0945-3245. Available under: doi: 10.1007/s00211-021-01264-xBibTex
@article{Burman2022Euler-55629.2,
year={2022},
doi={10.1007/s00211-021-01264-x},
title={Eulerian time-stepping schemes for the non-stationary Stokes equations on time-dependent domains},
volume={150},
issn={0029-599X},
journal={Numerische Mathematik},
pages={423--478},
author={Burman, Erik and Frei, Stefan and Massing, Andre},
note={The second author was supported by the DFG Research Scholarship FR3935/1-1.}
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The second author was supported by the DFG Research Scholarship FR3935/1-1.
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