  We present in detail three different quasi-Newton isogeometric algorithms for
the treatment of free boundary problems. Two algorithms are based on standard
Galerkin formulations, while the third is a fully-collocated scheme. With
respect to standard approaches, isogeometric analysis enables the accurate
description of curved geometries, and is thus particularly suitable for free
boundary numerical simulation. We apply the algorithms and compare their
performances to several benchmark tests, considering both Dirichlet and
periodic boundary conditions. In this context, iogeometric collocation turns
out to be robust and computationally more efficient than Galerkin. Our results
constitute a starting point of an in-depth analysis of the Euler equations for
incompressible fluids.

Numerical Analysis