Research reports

Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991

Local multigrid in H(curl)

by R. Hiptmair and W. Zheng

(Report number 2007-03)

Abstract
We consider H(curl)-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 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 H1-context along with local discrete Helmholtz-type decompositions of the edge element space.

Keywords: Edge elements, local multigrid, stable multilevel splittings, subspace correction theory, regular decompositions of H(curl), Helmholtz-type decompositions, local mesh refinement

@Techreport{HZ07_364,
  author = {R. Hiptmair and W. Zheng},
  title = {Local multigrid in H(curl)},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2007-03},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2007/2007-03.pdf },
  year = {2007}
}

Disclaimer
© Copyright for documents on this server remains with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use. The administrators respectfully request that authors inform them when any paper is published to avoid copyright infringement. Note that unauthorised copying of copyright material is illegal and may lead to prosecution. Neither the administrators nor the Seminar for Applied Mathematics (SAM) accept any liability in this respect. The most recent version of a SAM report may differ in formatting and style from published journal version. Do reference the published version if possible (see SAM Publications).