Title:         Multigrid preconditioning in H(div) on non-convex polygons

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

Source:        Computational and Applied Mathematics 17 (1998), pp. 307-319

Status:        Published

Abstract:  In an earlier paper we constructed and analyzed a multigrid
preconditioner for the system of linear algebraic equations arising from
the finite element discretization of boundary value problems associated
to the differential operator I - grad div.  In this paper we analyze the
procedure without assuming that the underlying domain is convex and show
that, also in this case, the preconditioner is spectrally equivalent to
the inverse of the discrete operator.

Keywords: preconditioner, finite element, multigrid, nonconvex domain

Subj. class.:  65N55, 65N30

URL:           http://ima.umn.edu/~arnold/papers/hdivn.pdf