Mathematical Methods in the Applied Sciences

Research Article

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

Corresponding Author

Helmut Harbrecht

Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

Correspondence to: Helmut Harbrecht, Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland.

E-mail: [email protected]

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Giannoula Mitrou,

Giannoula Mitrou

Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

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Helmut Harbrecht,

Corresponding Author

Helmut Harbrecht

Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

Correspondence to: Helmut Harbrecht, Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland.

E-mail: [email protected]

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Giannoula Mitrou,

Giannoula Mitrou

Mathematisches Institut, Universität Basel, Rheinsprung 21, 4051 Basel, Switzerland

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First published: 10 September 2014

https://doi.org/10.1002/mma.3268

Citations: 3

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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.Copyright © 2014 John Wiley & Sons, Ltd.

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Volume38, Issue13

15 September 2015

Pages 2850-2863

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

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

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