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Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data

Harbrecht, Helmut and Mitrou, Giannoula. (2015) Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data. Mathematical methods in the applied sciences, Vol. 38, H. 13. pp. 2850-2863.

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Official URL: http://edoc.unibas.ch/dok/A6419796

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Abstract

We apply the trial method for the solution of Bernoulli’s free boundary problem when the Dirichlet boundary condition is imposed for the solution of the underlying Laplace equation and the free boundary is updated according to the Neumann boundary condition. The Dirichlet boundary value problem for the Laplacian is solved by an exponentially convergent boundary element method. The update rule for the free boundary is derived from the linearization of the Neumann data around the actual free boundary. With the help of shape sensitivity analysis and Banach’s fixed-point theorem, we shed light on the convergence of the respective trial method. Especially, we derive a stabilized version of this trial method. Numerical examples validate the theoretical findings.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Computational Mathematics (Harbrecht)
UniBasel Contributors:Harbrecht, Helmut and Mitrou, Giannoula
Item Type:Article, refereed
Article Subtype:Research Article
Bibsysno:Link to catalogue
Publisher:John Wiley
ISSN:1099-1476
Note:Publication type according to Uni Basel Research Database: Journal article
Language:English
Identification Number:
Last Modified:31 Dec 2015 10:58
Deposited On:04 Sep 2015 14:30

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