Title: Preconditioning in H(div) and applications

Authors: D. N. Arnold, R. S. Falk, and R. Winther

Source: In P. Bjørstad, M. Espedal, and D. Keyes, editors, Ninth International
Conference on Domain Decomposition Methods, pages 12-19. DDM.org, 1996

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

URL: http://www.math.rutgers.edu/~falk/papers/hdivdd9.pdf