Skip to main content

Multigrid in H (div) and H (curl)

Summary. 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 \({\bf H (div)}\) and \({\bf H (curl)}\) 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.

This is a preview of subscription content, access via your institution.

Author information

Authors and Affiliations


Additional information

Received June 12, 1998 / Revised version received March 12, 1999 / Published online January 27, 2000

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Arnold, D., Falk, R. & Winther, R. Multigrid in H (div) and H (curl) . Numer. Math. 85, 197–217 (2000).

Download citation

  • Issue Date:

  • DOI:

  • Mathematics Subject Classification (1991):65N55, 65N30