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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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