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Auxiliary space preconditioning in H 0(curl; Ω)

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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.

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Authors and Affiliations

  1. SAM ETZ Zürich, 8092, Zürich

    R. Hiptmair & G. Widmer

  2. Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T, Hong Kong

    J. Zou

Authors
  1. R. Hiptmair
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  2. G. Widmer
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  3. J. Zou
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Corresponding author

Correspondence to R. Hiptmair.

Additional information

This author was fully supported by Hong Kong RGC grant (Project No. 403403)

This author acknowledges the support from a Direct Grant of CUHK during his visit at The Chinese University of Hong Kong.

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Hiptmair, R., Widmer, G. & Zou, J. Auxiliary space preconditioning in H 0(curl; Ω). Numer. Math. 103, 435–459 (2006). https://doi.org/10.1007/s00211-006-0683-0

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  • DOI: https://doi.org/10.1007/s00211-006-0683-0

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