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Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations

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  • Zhao, Jingjun
  • Zhao, Wenjiao
  • Xu, Yang

Abstract

This paper provides a Lagrange nodal discontinuous Galerkin method for solving the time-dependent incompressible space fractional Navier-Stokes equations numerically. The existence and uniqueness of weak solutions are obtained. By combining the Lagrange method in temporal discretization and the hybridized discontinuous Galerkin method in spatial direction, the fully discrete scheme is presented and the stability is proved rigorously. Furthermore, the error estimates for the L2-norm are derived in both the velocity and the pressure. Finally, some numerical experiments are given to illustrate the performance of the proposed method and validate the theoretical result.

Suggested Citation

  • Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2021. "Lagrange nodal discontinuous Galerkin method for fractional Navier-Stokes equations," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    • Handle: RePEc:eee:apmaco:v:391:y:2021:i:c:s0096300320306500
    DOI: 10.1016/j.amc.2020.125697
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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
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    Cited by:

    1. Maia, A.A.G. & Cavalca, D.F. & Tomita, J.T. & Costa, F.P. & Bringhenti, C., 2022. "Evaluation of an effective and robust implicit time-integration numerical scheme for Navier-Stokes equations in a CFD solver for compressible flows," Applied Mathematics and Computation, Elsevier, vol. 413(C).

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