Analysis of an SDG method for the incompressible Navier-stokes equations

Eric T. CHUNG; Weifeng QIU

doi:10.1137/15M1038694

Analysis of an SDG method for the incompressible Navier-stokes equations

Eric T. CHUNG, Weifeng QIU^*

^*Corresponding author for this work

Department of Mathematics

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

12 Citations (Scopus)

27 Downloads (CityUHK Scholars)

Abstract

In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier-Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.

Original language	English
Pages (from-to)	543-569
Journal	SIAM Journal on Numerical Analysis
Volume	55
Issue number	2
Online published	7 Mar 2017
DOIs	https://doi.org/10.1137/15M1038694
Publication status	Published - 2017

Research Keywords

Navier-Stokes equations
SDG

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COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2017 Society for Industrial and Applied Mathematics.

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abstract = "In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier-Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.",

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T1 - Analysis of an SDG method for the incompressible Navier-stokes equations

AU - CHUNG, Eric T.

AU - QIU, Weifeng

PY - 2017

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N2 - In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier-Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.

AB - In this paper, we analyze a staggered discontinuous Galerkin (SDG) method for the incompressible Navier-Stokes equations. The method is based on a novel splitting of the nonlinear convection term and results in a skew-symmetric discretization of it. As a result, the SDG discretization has a better conservation property and numerical stability property. The aim of this paper is to develop a mathematical theory for this method. In particular, we will show that the SDG method is well-posed and has an optimal rate of convergence. A superconvergence result will also be shown.

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DO - 10.1137/15M1038694

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1429

VL - 55

SP - 543

EP - 569

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 2

ER -

Analysis of an SDG method for the incompressible Navier-stokes equations

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GRF: New HDG Methods for Fluid Dynamics and Continuum Mechanics

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Analysis of an SDG method for the incompressible Navier-stokes equations

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GRF: New HDG Methods for Fluid Dynamics and Continuum Mechanics

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