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A Discontinuous Galerkin Method for the Coupled Stokes and Darcy Problem

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Abstract

Combining the mixed discontinuous Galerkin method for the Darcy flow and the interior penalty discontinuous Galerkin methods for the Stokes problem, a locally conservative discrete scheme is proposed for numerically solving the coupled Stokes and Darcy problem. We prove the well-posedness of the solution of the proposed numerical scheme by boundedness, K-ellipticity and a discrete inf-sup condition. A priori error estimates, in proper norms are derived, and to verify the theoretical analysis, some numerical experiments are given.

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Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

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Acknowledgements

We would like to acknowledge the financial support from the National Natural Science Foundation of China Grant No.11771348, 11971378, 51876170.

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

    Jing Wen, Jian Su, Yinnian He & Hongbin Chen

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  1. Jing Wen
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  2. Jian Su
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  3. Yinnian He
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  4. Hongbin Chen
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Correspondence to Hongbin Chen.

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Wen, J., Su, J., He, Y. et al. A Discontinuous Galerkin Method for the Coupled Stokes and Darcy Problem. J Sci Comput 85, 26 (2020). https://doi.org/10.1007/s10915-020-01342-6

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