In this paper we develop a staggered discontinuous Galerkin method for the Stokes and Darcy-Forchheimer problems coupled with the Beavers-Joseph-Saffman conditions. The method is defined by imposing staggered continuity for all the variables involved and the interface conditions are enforced by switching the roles of the variables met on the interface, which eliminate the hassle of introducing additional variables. This method can be flexibly applied to rough grids such as the highly distorted grids and the polygonal grids. In addition, the method allows nonmatching grids on the interface thanks to the special inclusion of the interface conditions, which is highly appreciated from a practical point of view. A new discrete trace inequality and a generalized Poincaré-Friedrichs inequality are proved, which enables us to prove the optimal convergence estimates under reasonable regularity assumptions. Finally, several numerical experiments are given to illustrate the performances of the proposed method, and the numerical results indicate that the proposed method is accurate and efficient, and in addition, it is a good candidate for practical applications.
Bibliographical noteFunding Information:
\ast Received by the editors June 14, 2019; accepted for publication (in revised form) August 31, 2020; published electronically January 4, 2021. https://doi.org/10.1137/19M1268525 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was partially supported by the Hong Kong RGC General Research Fund projects 14304217, 14302018, the CUHK Faculty of Science Direct grant 2018-19, and the NSFC/RGC Joint Research Scheme project HKUST620/15. The work of the third author was supported by the NRF grants 2015R1A5A1009350, 2019R1A2C2090021. The work of the fourth author was supported by the JSPS grant KAKENHI 18K13460 and JSPS A3 Foresight Program \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region, Hong Kong (email@example.com, firstname.lastname@example.org).
© 2021 Society for Industrial and Applied Mathematics.
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics