Abstract
The numerical approximation of the minimum problem: , is considered, where . The solution to this problem is a set A ⊆ Ω whose boundary has mean curvature κ and prescribed contact angle θ at ∂Ω. A front-tracking algorithm and a variational algorithm are presented, and a few numerical experiments illustrate their behaviour.
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G. Bellettini, M. Paolini, and C. Verdi, l’-convergence of discrete approximations to interfaces with prescribed mean curvature, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (9) (to appear).
G. Bellettini, M. Paolini, and C. Verdi, Numerical minimization of geometrical type problems related to calculus of variations,Calcolo (to appear).
E. De Giorgi, Free discontinuity problems in calculus of variations,“in Proc. Meeting in honour of J.L. Lions,” North-Holland, Amsterdam, 1988 (to appear).
H. Federer, “Geometric Measure Theory,” Springer-Verlag, Berlin, 1968.
R. Finn, “Equilibrium Capillary Surfaces,” Springer-Verlag, Berlin, 1986.
P.E. Gill and W. Murray, Newton-type methods for unconstrained and linearly constrained optimization., Mathematical Programming 7 (1974), 311–350.
L. Modica and S. Mortola, Un esempio di I’-convergenza, Boll. Un. Mat. Ital. (5) 14 B (1977), 285–299.
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© 1991 Springer Basel AG
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Bellettini, G., Paolini, M., Verdi, C. (1991). Front-Tracking and Variational Methods to Approximate Interfaces with Prescribed Mean Curvature. In: Neittaanmäki, P. (eds) Numerical Methods for Free Boundary Problems. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 99. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5715-4_6
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DOI: https://doi.org/10.1007/978-3-0348-5715-4_6
Publisher Name: Birkhäuser, Basel
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