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Additive Average Schwarz Method for a Crouzeix-Raviart Finite Volume Element Discretization of Elliptic Problems

  • Atle Loneland
  • Leszek Marcinkowski
  • Talal Rahman
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)

Abstract

In this paper we introduce an additive Schwarz method for a Crouzeix-Raviart Finite Volume Element (CRFVE) discretization of a second order elliptic problem with discontinuous coefficients, where the discontinuities are inside subdomains and across subdomain boundaries. The proposed methods depends linearly or quadratically on the mesh parameters Hh, i.e., depending on the distribution of the coefficient in the model problem, the parameters describing the convergence of the GMRES method used to solve the preconditioned system depends linearly or quadratically on the mesh parameters. Also, under certain restrictions on the distribution of the coefficient, the convergence of the GMRES method is independent of jumps in the coefficient.

Notes

Acknowledgements

This work was partially supported by Polish Scientific Grant 2011/01/ B/ST1/01179 (Leszek Marcinkowski).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Atle Loneland
    • 1
  • Leszek Marcinkowski
    • 2
  • Talal Rahman
    • 3
  1. 1.Department of InformaticsUniversity of BergenBergenNorway
  2. 2.Faculty of MathematicsUniversity of WarsawWarszawaPoland
  3. 3.Faculty of EngineeringBergen University CollegeBergenNorway

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