A Weak Galerkin Finite Element Method for the Navier-Stokes Equations

A Weak Galerkin Finite Element Method for the Navier-Stokes Equations

Year:    2018

Communications in Computational Physics, Vol. 23 (2018), Iss. 3 : pp. 706–746

Abstract

In this paper, a weak Galerkin finite element method (WGFEM) is proposed for solving the Navier-Stokes equations (NSEs). The existence and uniqueness of the WGFEM solution of NSEs are established. The WGFEM provides very accurate numerical approximations for both the velocity field and pressure field, even with very high Reynolds numbers. The salient feature is that the flexibility of the WGFEM for the choice of the order of the velocity and pressure comparing to the standard finite element methods. Optimal order error estimates in both |·|$W_h$ and $L^2$ norms are proved for the semi-discretized scheme. Numerical simulations are presented to show the efficiency of the WGFEM.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2016-0267

Communications in Computational Physics, Vol. 23 (2018), Iss. 3 : pp. 706–746

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    41

Keywords:    Weak Galerkin finite element method the Navier-Stokes equations.