  Isogeometric Analysis (IGA) is a computational technique for the numerical
approximation of partial differential equations (PDEs). This technique is based
on the use of spline-type basis functions, that are able to hold a global
smoothness and allow to exactly capture a wide set of common geometries. The
current rise of this approach has encouraged the search of fast solvers for
isogeometric discretizations and nowadays this topic is full of interest. In
this framework, a desired property of the solvers is the robustness with
respect to both the polinomial degree $p$ and the mesh size $h$. For this task,
in this paper we propose a two-level method such that a discretization of order
$p$ is considered in the first level whereas the second level consists of a
linear or quadratic discretization. On the first level, we suggest to apply one
single iteration of a multiplicative Schwarz method. The choice of the
block-size of such an iteration depends on the spline degree $p$, and is
supported by a local Fourier analysis (LFA). At the second level one is free to
apply any given strategy to solve the problem exactly. However, it is also
possible to get an approximation of the solution at this level by using an
$h-$multigrid method. The resulting solver is efficient and robust with respect
to the spline degree $p$. Finally, some numerical experiments are given in
order to demonstrate the good performance of the proposed solver.
