Multigrid in H(div) and H(curl)

We consider the solution of systems of linear algebraic equations which ari se from the finite element discretization of variational problems posed in the Hilbert spaces H (div) and H (curl) in three dimensions. We show that i f appropriate finite element spaces and appropriate additive or multiplicat ive Schwarz smoothers are used, then the multigrid V-cycle is an efficient solver and preconditioner for the discrete operator. All results ale unifor m with respect to the mesh size, the number of mesh levels, and weights on the two terms in the inner products. Mathematics Subject Classification (19 91): 65N55, 65N30.