Repository: Freie Universit├Ąt Berlin, Math Department

Numerical approximation of capillary surfaces in a negative gravitational field

Hardering, H. (2013) Numerical approximation of capillary surfaces in a negative gravitational field. Interfaces and Free Boundaries, 15 (3). pp. 263-280. ISSN 1463-9971

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Official URL: http://dx.doi.org/10.4171/IFB/303

Abstract

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.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Numerical Analysis
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics
ID Code:1898
Deposited By: Ekaterina Engel
Deposited On:13 Apr 2016 09:00
Last Modified:03 Mar 2017 14:42

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