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Staggered DG Method with Small Edges for Darcy Flows in Fractured Porous Media

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Abstract

In this paper, we present and analyze a staggered discontinuous Galerkin method for Darcy flows in fractured porous media on fairly general meshes. A staggered discontinuous Galerkin method and a standard conforming finite element method with appropriate inclusion of interface conditions are exploited for the bulk region and the fracture, respectively. Our current analysis works on fairly general polygonal elements even in the presence of small edges. We prove the optimal convergence estimates in \(L^2\) error for all the variables by exploiting the Ritz projection. Importantly, our error estimates are shown to be fully robust with respect to the heterogeneity and anisotropy of the permeability coefficients. Several numerical experiments including meshes with small edges and anisotropic meshes are carried out to confirm the theoretical findings. Finally, our method is applied in the framework of unfitted mesh.

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Acknowledgements

The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project Numbers 14304217 and 14302018), CUHK Faculty of Science Direct Grant 2019-20 and NSFC/RGC Joint Research Scheme (Project Number HKUST620/15). The research of Eun-Jae Park was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021).

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Authors and Affiliations

  1. Department of Mathematics, City University of Hong Kong, Kowloon Tong, Hong Kong SAR, China

    Lina Zhao

  2. Hong Kong Centre for Cerebro-Cardiovascular Health Engineering, Hong Kong SAR, China

    Dohyun Kim

  3. School of Mathematics and Computing, Computational Science and Engineering, Yonsei University, Seoul, 03722, Korea

    Eun-Jae Park

  4. Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR, China

    Eric Chung

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  1. Lina Zhao
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  2. Dohyun Kim
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Correspondence to Eun-Jae Park.

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Zhao, L., Kim, D., Park, EJ. et al. Staggered DG Method with Small Edges for Darcy Flows in Fractured Porous Media. J Sci Comput 90, 83 (2022). https://doi.org/10.1007/s10915-022-01760-8

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