A Discontinuous Galerkin Method for the Coupled Stokes and Darcy Problem

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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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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Keywords

  • Stokes and Darcy problem
  • Discontinuous Galerkin methods
  • Priori error estimates