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We propose and analyze a two-level method for mimetic finite differenceapproximations of second order elliptic boundary value problems. We prove thatthe two-level algorithm is uniformly convergent, i.e., the number of iterationsneeded to achieve convergence is uniformly bounded independently of thecharacteristic size of the underling partition. We also show that the resultingscheme provides a uniform preconditioner with respect to the number of degreesof freedom. Numerical results that validate the theory are also presented.

A Two-Level Method for Mimetic Finite Difference Discretizations of Elliptic Problems