Some DG schemes for the Stokes–Darcy problem using P1/P1 element

Japan Journal of Industrial and Applied Mathematics volume 36, pages1101–1128(2019)Cite this article

Abstract

We propose two new DG schemes based on the penalty and Nitsche’s methods respectively for the Stokes–Darcy problem, where we adopt the P1/P1 elements for both the Stokes and Darcy’s velocity/pressure. The well-posedness and a-priori estimates for the discrete solutions are established. The convergence order is elucidated by the numerical experiments.

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Author information

Affiliations

  1. Department of Applied Mathematics, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan

    Guanyu Zhou

  2. The Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

    Takahito Kashiwabara

  3. Graduate School of Business Administration, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo, 186-8603, Japan

    Issei Oikawa

  4. Department of Mathematics, The Chinese University of Hong Kong, Lady Shaw Building, Shatin, N.T., Hong Kong

    Eric Chung

  5. Department of Applied Mathematics, National Chiao Tung University, 2F, Science Bld. 1, 1001 Ta Hsueh Road, Hsinchu, 30010, Taiwan

    Ming-Cheng Shiue

Authors
  1. Guanyu Zhou
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  2. Takahito Kashiwabara
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  3. Issei Oikawa
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  4. Eric Chung
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  5. Ming-Cheng Shiue
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Correspondence to Guanyu Zhou.

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The research of G. Zhou was supported by JSPS KAKENHI 18K13460 and JSPS A3 Foresight Program. The research of T. Kashiwabara was supported by JSPS Grant-in-Aid for Young Scientists B 17K14230. The research of E. Chung was partially supported by the NSFC/RGC Joint Research Scheme (Project number HKUST620/15). M.-C. Shiue was supported in part by the Grant MOST-106-2115-M-009-011 -MY2.

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Zhou, G., Kashiwabara, T., Oikawa, I. et al. Some DG schemes for the Stokes–Darcy problem using P1/P1 element. Japan J. Indust. Appl. Math. 36, 1101–1128 (2019). https://doi.org/10.1007/s13160-019-00377-z

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Keywords

  • Finite element method
  • Stokes–Darcy problem
  • Penalty method
  • Discontinuous Galerkin method

Mathematics Subject Classification

  • Primary 65N30
  • Secondary 35Q30