  In this paper we consider approximations of Neumann problems for the integral
fractional Laplacian by continuous, piecewise linear finite elements. We
analyze the weak formulation of such problems, including their well-posedness
and asymptotic behavior of solutions. We address the convergence of the finite
element discretizations and discuss the implementation of the method. Finally,
we present several numerical experiments in one- and two-dimensional domains
that illustrate the method's performance as well as certain properties of
solutions.
