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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. China Department 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)
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Abstract

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 ℝ2. The nonlinear stability is proved for the proposed symmetric variational formulation. Moreover, for general triangulations the priori estimates for the L2–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 methods 65M15: Error bounds 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 1 , July 2017 , pp. 202 - 227
Copyright
Copyright © Global-Science Press 2017 

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Footnotes

Communicated by Chi-Wang Shu

References

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