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

10/07/2019
by   Erik Burman, et al.
0

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 L^2(L^2)-norm error bounds for the velocities. Finally, the theoretical results are substantiated with numerical examples.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset