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

Harbrecht, Helmut and Mitrou, Giannoula. (2013) Stabilization of the trial method for the Bernoulli problem in case of prescribed Dirichlet data. Preprints Fachbereich Mathematik, 2013 (29).

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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)
12 Special Collections > Preprints Fachbereich Mathematik
UniBasel Contributors:Harbrecht, Helmut and Mitrou, Giannoula
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:13 May 2019 05:30
Deposited On:28 Mar 2019 09:52

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