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Additive average Schwarz method for a Crouzeix–Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients

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Abstract

In this paper we introduce an additive Schwarz method for a Crouzeix–Raviart finite volume element discretization of a second order elliptic problem with discontinuous coefficients, where the discontinuities are both inside the subdomains and across and along the subdomain boundaries. We show that, depending on the distribution of the coefficient in the model problem, the parameters describing the generalized minimal residual method (GMRES) convergence rate of the proposed method depend linearly 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.

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Acknowledgments

The authors would like to thank Professor Petter Bjørstad and Professor Maksymilian Dryja for their valuable comments and discussions.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, 5020, Bergen, Norway

    A. Loneland

  2. Department of Computing, Mathematics and Physics, Bergen University College, 5063, Bergen, Norway

    A. Loneland & T. Rahman

  3. Faculty of Mathematics, University of Warsaw, Banacha 2, 02-097, Warszawa, Poland

    L. Marcinkowski

Authors
  1. A. Loneland
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  2. L. Marcinkowski
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  3. T. Rahman
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Corresponding author

Correspondence to A. Loneland.

Additional information

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

T. Rahman acknowledges the support from the NRC through the DAADppp project 233989.

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Loneland, A., Marcinkowski, L. & Rahman, T. Additive average Schwarz method for a Crouzeix–Raviart finite volume element discretization of elliptic problems with heterogeneous coefficients. Numer. Math. 134, 91–118 (2016). https://doi.org/10.1007/s00211-015-0771-0

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  • DOI: https://doi.org/10.1007/s00211-015-0771-0

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