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