A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Detail(s)

Original languageEnglish
Pages (from-to)163-179
Journal / PublicationComputers and Mathematics with Applications
Volume128
Online published28 Oct 2022
Publication statusPublished - 15 Dec 2022

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.

Research Area(s)

  • Divergence preserving velocity reconstruction, Polygonal mesh, Pressure-robustness, Staggered DG method, Superconvergence, The Stokes equations