Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients
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.
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First author has been supported by MINECO grant MTM2011-27739-C04-04 and 2009-SGR-345 from AGAUR-Generalitat de Catalunya. The work of the second and third authors was supported in part by NSF/DMS Awards 0715146 and 0915220, and by DOD/DTRA Award HDTRA-09-1-0036. The work of the fourth author was supported in part by the NSF/DMS Award 0810982.
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