Author:
Burman Erik,Frei Stefan,Massing Andre
Abstract
AbstractThis 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 $$L^2(L^2)$$
L
2
(
L
2
)
-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Computational Mathematics
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