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Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations

Part of:Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 May 2017

Shuqin Wang,
Weihua Deng,
Jinyun Yuan and
Yujiang Wu
Shuqin Wang*
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. ChinaDepartment of Mathematics, Federal University of Paraná, Centro Politécnico, CP: 19.081, Curitiba, CEP: 81531-990, PR, Brazil
Weihua Deng*
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
Jinyun Yuan*
Affiliation:
Department of Mathematics, Federal University of Paraná, Centro Politécnico, CP: 19.081, Curitiba, CEP: 81531-990, PR, Brazil
Yujiang Wu*
Affiliation:
School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China
*
*Corresponding author. Email addresses:wsqlzu@gmail.com (S. Wang), dengwh@lzu.edu.cn (W. Deng), yuanjy@gmail.com (J. Yuan), myjaw@lzu.edu.cn (Y.Wu)
*Corresponding author. Email addresses:wsqlzu@gmail.com (S. Wang), dengwh@lzu.edu.cn (W. Deng), yuanjy@gmail.com (J. Yuan), myjaw@lzu.edu.cn (Y.Wu)
*Corresponding author. Email addresses:wsqlzu@gmail.com (S. Wang), dengwh@lzu.edu.cn (W. Deng), yuanjy@gmail.com (J. Yuan), myjaw@lzu.edu.cn (Y.Wu)
*Corresponding author. Email addresses:wsqlzu@gmail.com (S. Wang), dengwh@lzu.edu.cn (W. Deng), yuanjy@gmail.com (J. Yuan), myjaw@lzu.edu.cn (Y.Wu)

Abstract

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By combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, variational formulations are established for time-dependent incompressible Navier-Stokes equations in ℝ 2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L 2–norm of the errors in both velocity and pressure are derived. Some numerical experiments are performed to verify theoretical results.

Keywords

Navier-Stokes equationslocal discontinuous Galerkin methodsymmetric variational formulation

MSC classification

Secondary:65M12: Stability and convergence of numerical methods65M15: Error bounds65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017, pp. 202 - 227
Copyright
Copyright © Global-Science Press 2017 

Footnotes

Communicated by Chi-Wang Shu

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