Finite Element Discretization of the Navier-Stokes Equations with a Free Capillary Surface - Bänsch, Eberhard (Numerische Mathematik, 2001)
The instationary Navier-Stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions. A stable finite element discretization is presented. The key idea is the treatment of the curvature terms by a variational formulation. In the context of a discontinuous in time space-time element discretization stability in (weak) energy norms can be proved. Numerical examples in 2 and 3 space dimensions are given.
UnivIS-Import:2015-03-09:Pub.2001.nat.dma.lama3.finite