Characteristic Local Discontinuous Galerkin Methods for Incompressible Navier-Stokes Equations

Authors

  • Shuqin Wang School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China.
  • Weihua Deng School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, P.R. China.
  • Jinyun Yuan Department of Mathematics, Federal University of Paran´a, Centro Politecnico, CP: 19.081, 81531-980 Curitiba, PR Brazil
  • Yujiang Wu School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu, P.R. China

DOI:

https://doi.org/10.4208/cicp.220515.031016a

Keywords:

Navier-Stokes equations, local discontinuous Galerkin method, symmetric variational formulation.

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.

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Published

2019-10-31

Issue

Vol. 22 No. 1 (2017)

Section

Articles