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Numerische Mathematik

, Volume 103, Issue 3, pp 435–459 | Cite as

Auxiliary space preconditioning in H 0(curl; Ω)

  • R. HiptmairEmail author
  • G. Widmer
  • J. Zou
Article

Abstract

We adapt the principle of auxiliary space preconditioning as presented in [J. Xu, The auxiliary space method and optimal multigrid preconditioning techniques for unstructured grids, Computing, 56 (1996), pp. 215–235.] to H (curl; ω)-elliptic variational problems discretized by means of edge elements. The focus is on theoretical analysis within the abstract framework of subspace correction. Employing a Helmholtz-type splitting of edge element vector fields we can establish asymptotic h-uniform optimality of the preconditioner defined by our auxiliary space method.

Mathematics Subject Classifications

65N22 65F10 65N30 65N55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.SAM ETZ ZürichZürich
  2. 2.Department of MathematicsThe Chinese University of Hong KongShatinHong Kong

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