Inscrição na biblioteca: Guest
Portal Digital Begell Biblioteca digital da Begell eBooks Diários Referências e Anais Coleções de pesquisa
International Journal for Uncertainty Quantification
Fator do impacto: 3.259 FI de cinco anos: 2.547 SJR: 0.417 SNIP: 0.8 CiteScore™: 1.52

ISSN Imprimir: 2152-5080
ISSN On-line: 2152-5099

Open Access

International Journal for Uncertainty Quantification

DOI: 10.1615/Int.J.UncertaintyQuantification.2017019550
pages 335-353

ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY

M. Dambrine
Université de Pau et des Pays de l'Adour, IPRA-LMA, UMR CNRS 5142 Avenue de l'université, 64000 Pau, France
Helmut Harbrecht
Universität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, 4051 Basel, Switzerland
M. D. Peters
Universität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, 4051 Basel, Switzerland
B. Puig
Université de Pau et des Pays de l'Adour, IPRA-LMA, UMR CNRS 5142 Avenue de l'université, 64000 Pau, France

RESUMO

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.


Articles with similar content:

Solving the 3D Maxwell Equations Near Conical Singularities by a Multiscale Strategy
International Journal for Multiscale Computational Engineering, Vol.7, 2009, issue 5
Franck Assous, Patrick Ciarlet, Jr.
ITERATIVE GLOBAL-LOCAL APPROACH TO CONSIDER THE EFFECTS OF LOCAL ELASTO-PLASTIC DEFORMATIONS IN THE ANALYSIS OF THIN-WALLED MEMBERS
International Journal for Multiscale Computational Engineering, Vol.15, 2017, issue 2
Ali Saleh, R. Emre Erkmen
OVERALL ELASTIC PROPERTIES OF POLYSILICON FILMS: A STATISTICAL INVESTIGATION OF THE EFFECTS OF POLYCRYSTAL MORPHOLOGY
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 3
Roberto Martini, Alberto Corigliano, Stefano Mariani, Marco Beghi, Aldo Ghisi
FRACTIONAL DIFFERENTIAL CALCULUS FOR 3D MECHANICALLY BASED NON-LOCAL ELASTICITY
International Journal for Multiscale Computational Engineering, Vol.9, 2011, issue 5
Massimiliano Zingales, Mario Di Paola
FINITE ELEMENT MODELING OF RADIATION HEAT TRANSFER COUPLED WITH CONDUCTION WITH SURFACE BOUNDARY EVOLUTION
International Heat Transfer Conference 10, Vol.5, 1994, issue
J.-V. Daurelle, R. Occelli , R. Martin