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Parallel Solution of Partial Differential Equations pp 181–208Cite as

Overlapping and Multilevel Schwarz Methods for Vector Valued Elliptic Problems in Three Dimensions

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Part of the The IMA Volumes in Mathematics and its Applications book series (IMA,volume 120)

Abstract

This paper is intended as a survey of current results on algorithmic and theoretical aspects of overlapping Schwarz methods for discrete H(curl;Ω) and H(div;Ω)-elliptic problems set in suitable finite element spaces. The emphasis is on a unified framework for the motivation and theoretical study of the various approaches developed in recent years.

Key words

  • Schwarz methods
  • domain decomposition
  • multilevel methods
  • multi-grid
  • Raviart–Thomas finite elements
  • Nédélec’s finite elements

This work was supported in part by the National Science Foundation under Grant NSF-ECS-9527169 and in part by the U.S. Department of Energy under Contract DEFG02-92ER25127.

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Author information

Authors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, USA

    Ralf Hiptmair

  2. Courant Institute, New York University, New York, NY, 10012, USA

    Andrea Toselli

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  1. Ralf Hiptmair
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  2. Andrea Toselli
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Editor information

Editors and Affiliations

  1. Institutt for Informatikk Hoyteknologisenteret, University of Bergen, Bergen, N-5020, Norway

    Petter Bjørstad

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

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Hiptmair, R., Toselli, A. (2000). Overlapping and Multilevel Schwarz Methods for Vector Valued Elliptic Problems in Three Dimensions. In: Bjørstad, P., Luskin, M. (eds) Parallel Solution of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 120. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1176-1_8

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