Geodesic
Numerical approximation of capillary surfaces in a negative gravitational field
Hanne Hardering1
1Freie Universität Berlin, Germany
Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 263-280

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DOI

A capillary surface in a negative gravitational field describes the shape of the surface of a hanging drop in a capillary tube with wetting material on the bottom. Mathematical modeling leads to the volume- and obstacle-constrained minimization of a nonconvex nonlinear energy functional of mean curvature type which is unbounded from below. In 1984 Huisken proved the existence and regularity of local minimizers of this energy under the condition on gravitation being sufficiently weak. We prove convergence of a first order finite element approximation of these minimizers. Numerical results demonstrating the theoretic convergence order are given.
DOI : 10.4171/ifb/303
Classification : 65-XX, 53-XX
Mots-clés : Capillary surface, obstacle problem, finite elements, discretization error bound

Hanne Hardering  1

1 Freie Universität Berlin, Germany 
Hanne Hardering. Numerical approximation of capillary surfaces in a negative gravitational field. Interfaces and free boundaries, Tome 15 (2013) no. 3, pp. 263-280. doi: 10.4171/ifb/303
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     number = {3},
     doi = {10.4171/ifb/303},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/303/}
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