Deparpartment of Mathematics

Penn State University

University Park, PA 16802

Deparpartment of Mathematics

Rutgers University

New Brunswick, NJ 08903

Department of Informatics

University of Oslo

Oslo, Norway

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

Subject classification: 65N55, 65N30

Contributed February 28, 1997.