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Two-Level Schwarz Methods for a Discontinuous Galerkin Approximation of Elliptic Problems with Jump Coefficients

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Abstract

We present two-level nonoverlapping and overlapping Schwarz preconditioners for the linear algebraic system arising from the weighted symmetric interior penalty Galerkin approximation of elliptic problems with highly heterogeneous coefficients. The coarse space is constructed by the local Dirichlet-to-Neumann maps the theoretical results show that the condition number of the preconditioned system is independent of the discontinuous coefficient, the number of subdomains and the mesh size for the nonoverlapping case. For the overlapping case adding an extra assumption of coefficient distribution, the similar conclusion is also obtained. Numerical experiments validate the theoretical results and illustrate the performance and robustness of the proposed two-level methods.

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The authors confirm that the data supporting the findings of this study are available within the article.

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Acknowledgements

The work of Yingzhi Liu and Yinnian He was supported by NSF of China (No. 11771348).

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  1. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Yingzhi Liu & Yinnian He

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  1. Yingzhi Liu
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Correspondence to Yinnian He.

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Liu, Y., He, Y. Two-Level Schwarz Methods for a Discontinuous Galerkin Approximation of Elliptic Problems with Jump Coefficients. J Sci Comput 84, 14 (2020). https://doi.org/10.1007/s10915-020-01257-2

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  • DOI: https://doi.org/10.1007/s10915-020-01257-2

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