Title:         Preconditioning in H(div) and applications

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

Source:        in: "Ninth International Conference on Domain Decomposition Methods
(Bergen, 1996)" (P. Bjorstad, M. Espedal, and D. Keyes, eds.), DDM.org, 1998, pp. 12-19

Status:        Published

Abstract:  Summarizing the work of [1], we show how to construct
preconditioners using domain decomposition and multigrid techniques for
the system of linear algebraic equations which arises from the finite
element discretization of boundary value problems associated to the
differential operator I - grad div.  These preconditioners are shown
to be spectrally equivalent to the inverse of the operator and thus
may be used to precondition iterative methods so that any given error
reduction may be achieved in a finite number of iterations independent
of the mesh discretization. We describe applications of these results
to the efficient solution of mixed and least squares finite element
approximations of elliptic boundary value problems.

Keywords: preconditioner, mixed method, least squares, finite element,
multigrid, domain decomposition

Subj. class.:  65N55, 65N30

URL:           http://ima.umn.edu/~arnold/papers/hdivdd9.pdf