Solution of free boundary problems in the presence of geometric uncertainties

The present article is concerned with solving Bernoulli’s exterior free boundary problem in case of an interior boundary which is random. We model this random free boundary problem such that the expectation and the variance of the sought domain can be defined. In order to numerically approximate the expectation and the variance, we propose a sampling method like the (quasi-) Monte Carlo quadrature. The free boundary is determined for each sample by the trial method which is a fixed-point like iteration. Extensive numerical results are given in order to illustrate the model.