Multigrid Preconditioning in H(div) on Non-Convex Polygons

Douglas N. Arnold
Deparpartment of Mathematics
Penn State University
University Park, PA 16802

Richard S. Falk
Deparpartment of Mathematics
Rutgers University
New Brunswick, NJ 08903

Ragnar Winther
Department of Informatics
University of Oslo
Oslo, Norway

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

Subject classification: 65N55, 65N30


Contributed February 28, 1997.