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

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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.

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Authors and Affiliations

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

    Eberhard Bänsch

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  1. Eberhard Bänsch
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Received March 26, 1999 / Revised version received October 12, 1999 / Published online November 8, 2000

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Bänsch, E. Finite element discretization of the Navier–Stokes equations with a free capillary surface. Numer. Math. 88, 203–235 (2001). https://doi.org/10.1007/PL00005443

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  • DOI: https://doi.org/10.1007/PL00005443

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