Geodesic
A second order convergent trial method for a free boundary problem in three dimensions
Monica Bugeanu1 ; Helmut Harbrecht1
1Universität Basel, Switzerland
Interfaces and free boundaries, Tome 17 (2015) no. 4, pp. 517-537

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DOI

The present article is concerned with the solution of a generalized Bernoulli free boundary problem in three spatial dimensions. We parametrize the free boundary under consideration over the sphere and apply a trial method which updates the free boundary into the normal direction. At the free boundary, we prescribe the Neumann boundary condition and update the free boundary with the help of the remaining Dirichlet boundary condition. An inexact Newton update is employed which leads to a novel second order convergent trial method. Numerical examples show the feasibility of the present approach. In particular, a parametric representation is utilized which imposes no restriction to the free boundary under consideration except for its genus.
DOI : 10.4171/ifb/352
Classification : 65-XX, 35-XX
Mots-clés : Free boundary problem, trial method, second order convergence

Monica Bugeanu  1   ; Helmut Harbrecht  1

1 Universität Basel, Switzerland 
Monica Bugeanu; Helmut Harbrecht. A second order convergent trial method for a free boundary problem in three dimensions. Interfaces and free boundaries, Tome 17 (2015) no. 4, pp. 517-537. doi: 10.4171/ifb/352
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     title = {A second order convergent trial method for a free boundary problem in three dimensions},
     journal = {Interfaces and free boundaries},
     pages = {517--537},
     year = {2015},
     volume = {17},
     number = {4},
     doi = {10.4171/ifb/352},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/352/}
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