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Numerische Mathematik

, Volume 88, Issue 2, pp 203–235 | Cite as

Finite element discretization of the Navier–Stokes equations with a free capillary surface

  • Eberhard Bänsch
Orignial article

Summary.

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.

Mathematics Subject Classification (1991): 35Q30, 65M12, 65M60, 76D05, 76D45 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Eberhard Bänsch
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany; e-mail: baensch@wias-berlin.de DE

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