  In this paper, we present a multigrid preconditioner for solving the linear
system arising from the piecewise linear nonconforming Crouzeix-Raviart
discretization of second order elliptic problems with jump coefficients. The
preconditioner uses the standard conforming subspaces as coarse spaces.
Numerical tests show both robustness with respect to the jump in the
coefficient and near-optimality with respect to the number of degrees of
freedom.
