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Auxiliary space preconditioning in H 0(curl; Ω)

Hiptmair, R. ; Widmer, G. ; Zou, J.

In: Numerische Mathematik, 2006, vol. 103, no. 3, p. 435-459

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    Titre
    • Auxiliary space preconditioning in H 0(curl; Ω)
    Auteur
    • Hiptmair, R.. SAM ETZ Zürich, 8092, Zürich
    • Widmer, G.. SAM ETZ Zürich, 8092, Zürich
    • Zou, J.. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T, Hong Kong
    Type de document
    • Postprint
    Classification
    • Informatique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:315703
    Summary
    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