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Local Multigrid in H(Curl)

Local Multigrid in H(Curl)
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Year:    2009

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 573–603

Abstract

We consider $\boldsymbol{H}$(curl, $Ω$)-elliptic variational problems on bounded Lipschitz polyhedra and their finite element Galerkin discretization by means of lowest order edge elements. We assume that the underlying tetrahedral mesh has been created by successive local mesh refinement, either by local uniform refinement with hanging nodes or bisection refinement. In this setting we develop a convergence theory for the the so-called local multigrid correction scheme with hybrid smoothing. We establish that its convergence rate is uniform with respect to the number of refinement steps. The proof relies on corresponding results for local multigrid in a $H^1(Ω)$-context along with local discrete Helmholtz-type decompositions of the edge element space.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.27.5.012

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 5 : pp. 573–603

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    31

Keywords:    Edge elements Local multigrid Stable multilevel splittings Subspace correction theory Regular decompositions of $\boldsymbol{H}(curl Ω)$ Helmholtz-type decompositions Local mesh refinement.

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