A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Lina Zhao; Eun Jae Park; Eric Chung

doi:10.1016/j.camwa.2022.10.019

A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Lina Zhao, Eun Jae Park, Eric Chung

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	163-179
Number of pages	17
Journal	Computers and Mathematics with Applications
Volume	128
DOIs	https://doi.org/10.1016/j.camwa.2022.10.019
Publication status	Published - 2022 Dec 15

Bibliographical note

Funding 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 ).

Publisher Copyright:
© 2022

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computational Theory and Mathematics
Computational Mathematics

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10.1016/j.camwa.2022.10.019

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title = "A pressure robust staggered discontinuous Galerkin method for the Stokes equations",

abstract = "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.",

author = "Lina Zhao and Park, {Eun Jae} and Eric Chung",

note = "Funding 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 ). Publisher Copyright: {\textcopyright} 2022",

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AU - Zhao, Lina

AU - Park, Eun Jae

AU - Chung, Eric

N1 - Funding 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 ). Publisher Copyright: © 2022

PY - 2022/12/15

Y1 - 2022/12/15

N2 - 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.

AB - 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.

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JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

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A pressure robust staggered discontinuous Galerkin method for the Stokes equations

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