RT Journal Article
ID 1b343cae2ff588e4
A1 Dambrine, M.
A1 Harbrecht, Helmut
A1 Peters, M. D.
A1 Puig, B.
T1 ON BERNOULLI'S FREE BOUNDARY PROBLEM WITH A RANDOM BOUNDARY
JF International Journal for Uncertainty Quantification
JO IJUQ
YR 2017
FD 2017-08-24
VO 7
IS 4
SP 335
OP 353
K1 Bernoulli's free boundary problem
K1 random boundary
AB 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.
PB Begell House
LK http://dl.begellhouse.com/journals/52034eb04b657aea,0ce170d9609cac4a,1b343cae2ff588e4.html