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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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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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  • DOI: https://doi.org/10.1007/978-1-4612-1176-1_8

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