Schwarz Methods for a Crouzeix-Raviart Finite Volume Discretization of Elliptic Problems

Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 104)


In this paper, we present two variants of the Additive Schwarz Method (ASM) for a Crouzeix-Raviart finite volume (CRFV) discretization of the second order elliptic problem with discontinuous coefficients, where the discontinuities are only across subdomain boundaries. The resulting system, which is nonsymmetric, is solved using the preconditioned GMRES iteration, where in one variant of the ASM the preconditioner is symmetric while in the other variant it is nonsymmetric. The proposed methods are almost optimal, in the sense that the convergence of the GMRES iteration, in the both cases, depend only poly-logarithmically on the mesh parameters.


Additive Schwarz method Crouzeix-Raviart finite element Domain decomposition Finite volume method 



This work was partially supported by Polish Scientific Grant 2011/01/B/ ST1/01179 and Chinese Academy of Science Project: 2013FFGA0009 - GJHS20140901004635677.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Leszek Marcinkowski
    • 1
  • Atle Loneland
    • 2
  • Talal Rahman
    • 2
  1. 1.Faculty of MathematicsUniversity of WarsawWarszawaPoland
  2. 2.Department of Computing, Mathematics, and PhysicsBergen University CollegeBergenNorway

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