An equal-order hybridized discontinuous Galerkin method with a small pressure penalty parameter for the Stokes equations. (1st July 2021)

• Record Type: Journal Article
• Authors: Hou, Yanren; Han, Yongbin; Wen, Jing
• Is Part Of: Computers & mathematics with applications. Volume 93(2021)
• Page Start: 58
• Page End: 65
• Publication Date: 2021-07-01
• Subjects: Equal-order -- Hybridized discontinuous Galerkin method -- Pressure-robust -- Stokes equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2021.03.031
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: In this paper, an equal-order hybridized discontinuous Galerkin (HDG) method with a small pressure penalty parameter for the Stokes equations is analyzed. When the pressure penalty parameter γ tends to 0 ( γ > 0 ), the velocity approximation tends to be H(div)-conforming and exactly divergence-free, and the velocity error bound tends to be pressure-robust. However, taking the value of γ too small will cause the over-stabilization of the pressure. Then, we can provide a post-processing procedure to obtain a stable pressure approximation.