A black-box multigrid preconditioner for the biharmonic equation (Q1826456)

Mixed finite element discretizations of biharmonic equations lead to saddle point systems. The paper considers a conventional and a constraint block preconditioner for such systems. The condition numbers of the preconditioned systems are studied. Numerical tests with the exact and two inexact versions of the constraint block preconditioner are presented. The inexact versions approximate a discrete Laplacian by a number of multigrid V-cycles. The iteration number of a preconditioned BICGSTAB(2) method tends to grow slowly with mesh refinement, \(O(h^{-1/2})\), for the exact version and in the case that sufficiently many multigrid cycles are applied in the inexact version.