On bernoulli’s free boundary problem with a random boundary - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal for Uncertainty Quantification Année : 2017

On bernoulli’s free boundary problem with a random boundary

Résumé

This article is dedicated to the solution of Bernoulli's exterior free boundary problem in the situation of a random interior boundary. We provide the theoretical background that ensures the well-posedness of the problem under consideration and describe two different frameworks to define the expectation and the deviation of the resulting annular domain. The first approach is based on the Vorob'ev expectation, which can be defined for arbitrary sets. The second approach is based on the particular parametrization. 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.

Dates et versions

hal-01759860 , version 1 (05-04-2018)

Identifiants

Citer

Marc Dambrine, H. Harbrecht, M.D. Peters, Bénédicte Puig. On bernoulli’s free boundary problem with a random boundary. International Journal for Uncertainty Quantification, 2017, 7 (4), pp.335-353. ⟨10.1615/Int.J.UncertaintyQuantification.2017019550⟩. ⟨hal-01759860⟩
35 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More