In this paper, we propose a pressure robust staggered discontinuous Galerkin method for the Stokes equations on general polygonal meshes by using piecewise constant approximations. We modify the right-hand side of the body force in the discrete formulation by exploiting a divergence preserving velocity reconstruction operator, which is the crux for pressure-independent velocity error estimates. The optimal convergence for the velocity gradient, velocity, and pressure is proved. In addition, we can establish the superconvergence of the velocity approximation by incorporating a divergence preserving velocity reconstruction operator in the dual problem, which is also an essential contribution of this paper. Finally, several numerical experiments are carried out to confirm the theoretical findings.
|Number of pages||17|
|Journal||Computers and Mathematics with Applications|
|Publication status||Published - 2022 Dec 15|
Bibliographical noteFunding Information:
The research of Lina Zhao is supported by a grant from City University of Hong Kong (Project No. 7200699 ). The research of Eric Chung is partially supported by the Hong Kong RGC General Research Fund (Project numbers 14304719 and 14302620 ) and CUHK Faculty of Science Direct Grant 2020-21 . The research of Eun-Jae Park is supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT ( NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021 ).
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics