An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains

Abstract

We analyse a Eulerian Finite Element method, combining a Eulerian time-stepping scheme applied to the time-dependent Stokes equations using the CutFEM approach with inf-sup stable Taylor-Hood elements for the spatial discretisation. This is based on the method introduced by Lehrenfeld \& Olshanskii [ESAIM: M2AN 53(2):585--614] in the context of a scalar convection-diffusion problems on moving domains, and extended to the non-stationary Stokes problem on moving domains by Burman, Frei \& Massing [arXiv:1910.03054 [math.NA]] using stabilised equal-order elements. The analysis includes the geometrical error made by integrating over approximated levelset domains in the discrete CutFEM setting. The method is implemented and the theoretical results are illustrated using numerical examples.

References in corpus (2)

• An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
• Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations

Cited by in corpus (12)

• An unfitted Eulerian finite element method for the time-dependent Stokes problem on moving domains
• Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data
• Geometrically Higher Order Unfitted Space-Time Methods for PDEs on Moving Domains
• CutFEM and ghost stabilization techniques for higher order space-time discretizations of the Navier-Stokes equations
• Using a deep neural network to predict the motion of under-resolved triangular rigid bodies in an incompressible flow
• An Eulerian finite element method for the linearized Navier--Stokes problem in an evolving domain
• Stability of instantaneous pressures in an Eulerian finite element method for moving boundary flow problems
• Error analysis for a parabolic PDE model problem on a coupled moving domain in a fully Eulerian framework
• An evolving space framework for Oseen equations on a moving domain
• An unfitted finite element method for two-phase Stokes problems with slip between phases
• A conservative Eulerian finite element method for transport and diffusion in moving domains
• Geometry Error Analysis of a parametric mapping for Higher Order Unfitted Space-Time Methods