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

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

Source: Comput. Appl. Math., 17(3):303-315, 1998

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 

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