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On Bernoulli's free boundary problem with a random boundary

Dambrine, Marc and Harbrecht, Helmut and Peters, Michael and Puig, Benedicte. (2016) On Bernoulli's free boundary problem with a random boundary. Preprints Fachbereich Mathematik, 2016 (31).

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Abstract

This article is dedicated to the solution of Bernoulli’s exterior free boundary problem in the situation of a random interior boundary. We describe two different frameworks to define the expectation and the deviation of the resulting annular domain. In order to compare these approaches, we present analytical examples for the case of a circular interior boundary. Additionally, numerical experiments are performed for more general geometric configurations. For the numerical approximation of the expectation and the deviation, we propose a sampling method like the Monte Carlo or the quasi-Monte Carlo quadrature. Each particular realization of the free boundary is then computed by the trial method, which is a fixed-point like iteration for the solution of Bernoulli's free boundary problem.
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 Peters, Michael
Item Type:Preprint
Publisher:Universität Basel
Language:English
Last Modified:21 Apr 2019 22:28
Deposited On:28 Mar 2019 09:51

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