Analysis of the Staggered DG Method for the Quasi-Newtonian Stokes flows

Jingyu Liu; Yang Liu; Lina Zhao

doi:10.1007/s10915-024-02741-9

Analysis of the Staggered DG Method for the Quasi-Newtonian Stokes flows

Jingyu Liu, Yang Liu, Lina Zhao

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and eliminates the pressure variable via the incompressibility condition. Thanks to the subtle construction of the finite element spaces used in our staggered DG method, no additional numerical flux or stabilization terms are needed. Based on the abstract theory for the non-linear twofold saddle point problems, we prove the well-posedness of our scheme. A priori error analysis for all the involved unknowns is also provided. In addition, the proposed scheme can be hybridizable and the global problem only involves the trace variables, rendering the method computationally attractive. Finally, several numerical experiments are carried out to illustrate the performance of our scheme. © The Author(s) 2024.

Original language	English
Article number	14
Journal	Journal of Scientific Computing
Volume	102
Issue number	1
Online published	20 Nov 2024
DOIs	https://doi.org/10.1007/s10915-024-02741-9
Publication status	Published - Jan 2025

Funding

Open access publishing enabled by City University of Hong Kong Library's agreement with Springer Nature. The research of Lina Zhao is partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China. [Project No. 21309522].

Research Keywords

Discontinuous Galerkin methods
Hybridization
Polygonal mesh
Quasi-Newtonian Stokes flow

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This full text is made available under CC-BY 4.0. https://creativecommons.org/licenses/by/4.0/

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abstract = "This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and eliminates the pressure variable via the incompressibility condition. Thanks to the subtle construction of the finite element spaces used in our staggered DG method, no additional numerical flux or stabilization terms are needed. Based on the abstract theory for the non-linear twofold saddle point problems, we prove the well-posedness of our scheme. A priori error analysis for all the involved unknowns is also provided. In addition, the proposed scheme can be hybridizable and the global problem only involves the trace variables, rendering the method computationally attractive. Finally, several numerical experiments are carried out to illustrate the performance of our scheme. {\textcopyright} The Author(s) 2024.",

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N2 - This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and eliminates the pressure variable via the incompressibility condition. Thanks to the subtle construction of the finite element spaces used in our staggered DG method, no additional numerical flux or stabilization terms are needed. Based on the abstract theory for the non-linear twofold saddle point problems, we prove the well-posedness of our scheme. A priori error analysis for all the involved unknowns is also provided. In addition, the proposed scheme can be hybridizable and the global problem only involves the trace variables, rendering the method computationally attractive. Finally, several numerical experiments are carried out to illustrate the performance of our scheme. © The Author(s) 2024.

AB - This paper introduces and analyzes a staggered discontinuous Galerkin (DG) method for quasi-Newtonian Stokes flow problems on polytopal meshes. The method introduces the flux and tensor gradient of the velocity as additional unknowns and eliminates the pressure variable via the incompressibility condition. Thanks to the subtle construction of the finite element spaces used in our staggered DG method, no additional numerical flux or stabilization terms are needed. Based on the abstract theory for the non-linear twofold saddle point problems, we prove the well-posedness of our scheme. A priori error analysis for all the involved unknowns is also provided. In addition, the proposed scheme can be hybridizable and the global problem only involves the trace variables, rendering the method computationally attractive. Finally, several numerical experiments are carried out to illustrate the performance of our scheme. © The Author(s) 2024.

KW - Discontinuous Galerkin methods

KW - Hybridization

KW - Polygonal mesh

KW - Quasi-Newtonian Stokes flow

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Analysis of the Staggered DG Method for the Quasi-Newtonian Stokes flows

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Analysis of the Staggered DG Method for the Quasi-Newtonian Stokes flows

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Funding

Research Keywords

Publisher's Copyright Statement

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ECS: Unfitted Numerical Schemes for Fluid-structure Interaction and Applications

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