419 research outputs found
Hybridized CutFEM for Elliptic Interface Problems
We design and analyze a hybridized cut finite element method for elliptic
interface problems. In this method very general meshes can be coupled over
internal unfitted interfaces, through a skeletal variable, using a Nitsche type
approach. We discuss how optimal error estimates for the method are obtained
using the tools of cut finite element methods and prove a condition number
estimate for the Schur complement. Finally, we present illustrating numerical
examples
A CutFEM method for two-phase flow problems
In this article, we present a cut finite element method for two-phase
Navier-Stokes flows. The main feature of the method is the formulation of a
unified continuous interior penalty stabilisation approach for, on the one
hand, stabilising advection and the pressure-velocity coupling and, on the
other hand, stabilising the cut region. The accuracy of the algorithm is
enhanced by the development of extended fictitious domains to guarantee a well
defined velocity from previous time steps in the current geometry. Finally, the
robustness of the moving-interface algorithm is further improved by the
introduction of a curvature smoothing technique that reduces spurious
velocities. The algorithm is shown to perform remarkably well for low capillary
number flows, and is a first step towards flexible and robust CutFEM algorithms
for the simulation of microfluidic devices
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