Title: Multigrid in H(div) and H(curl)

Authors: Douglas N. Arnold, Richard S. Falk, and Ragnar Winther

Source: Numer. Math., 85(2):197-217, 2000

Abstract:    We consider the solution of systems of linear algebraic equations
    which arise from the finite element discretization of variational
    problems posed in the Hilbert spaces H(div) and H(curl) in three
    dimensions. We show that if appropriate finite element spaces and
    appropriate additive or multiplicative Schwarz smoothers are used,
    then the multigrid V-cycle is an efficient solver and
    preconditioner for the discrete operator. All results are uniform
    with respect to the mesh size, the number of mesh levels, and
    weights on the two terms in the inner products.

Keywords: multigrid, preconditioner, mixed method, finite element

URL: http://www.math.rutgers.edu/~falk/papers/hdivcurl.pdf