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Nonoverlapping Three Grid Additive Schwarz for hp-DGFEM with Discontinuous Coefficients

  • Piotr KrzyżanowskiEmail author
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 125)

Abstract

We discuss a nonoverlapping additive Schwarz method for an h-p DGFEM discretization of an elliptic PDE with discontinuous coefficients, where the fine grid is decomposed into subdomains of size H and the coarse grid consists of cells size \(\mathcal {H}\) such that \(h\leq H \leq \mathcal {H}\). We prove the condition number is \(O(p^2/q)\cdot O(\mathcal {H}^2/Hh)\) and is independent from the jumps of the coefficient if the discontinuities are aligned with the coarse grid.

Notes

Acknowledgements

The author wishes to thank two anonymous referees whose comments and remarks helped to improve the paper substantially. This research has been partially supported by the Polish National Science Centre grant 2016/21/B/ST1/00350.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of WarsawWarszawaPoland

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