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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
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.
-
A pressure-robust stabilizer-free WG finite element method for the Stokes equations on simplicial grids
Yang, Yan | Ye, Xiu | Zhang, ShangyouElectronic Research Archive, Vol. 32 (2024), Iss. 5 P.3413
https://doi.org/10.3934/era.2024158 [Citations: 0] -
An Upwind Weak Galerkin Scheme for Convection-Dominated Oseen Equations
Qi, Wenya | Wang, JunpingCommunications on Applied Mathematics and Computation, Vol. (2024), Iss.
https://doi.org/10.1007/s42967-024-00438-2 [Citations: 0] -
A Robust Numerical Method for the Random Interface Grating Problem via Shape Calculus, Weak Galerkin Method, and Low-Rank Approximation
Bao, Gang | Cao, Yanzhao | Hao, Yongle | Zhang, KaiJournal of Scientific Computing, Vol. 77 (2018), Iss. 1 P.419
https://doi.org/10.1007/s10915-018-0712-z [Citations: 5] -
A modified weak Galerkin method for (curl)-elliptic problem
Tang, Ming | Zhong, Liuqiang | Xie, YingyingComputers & Mathematics with Applications, Vol. 139 (2023), Iss. P.224
https://doi.org/10.1016/j.camwa.2022.09.018 [Citations: 2] -
An adaptive weak Galerkin finite element method with hierarchical bases for the elliptic problem
Zhang, Jiachuan | Li, Jingshi | Li, Jingzhi | Zhang, KaiNumerical Methods for Partial Differential Equations, Vol. 36 (2020), Iss. 6 P.1280
https://doi.org/10.1002/num.22473 [Citations: 4] -
A locking-free weak Galerkin finite element method for linear elasticity problems
Huo, Fuchang | Wang, Ruishu | Wang, Yanqiu | Zhang, RanComputers & Mathematics with Applications, Vol. 160 (2024), Iss. P.181
https://doi.org/10.1016/j.camwa.2024.02.032 [Citations: 1] -
Two-Order Superconvergent CDG Finite Element Method for the Heat Equation on Triangular and Tetrahedral Meshes
Ye, Xiu | Zhang, ShangyouCommunications on Applied Mathematics and Computation, Vol. (2024), Iss.
https://doi.org/10.1007/s42967-024-00444-4 [Citations: 0] -
Interpolated coefficients stabilizer-free weak Galerkin method for semilinear parabolic convection–diffusion problem
Li, Wenjuan | Gao, Fuzheng | Cui, JintaoApplied Mathematics Letters, Vol. 159 (2025), Iss. P.109268
https://doi.org/10.1016/j.aml.2024.109268 [Citations: 0] -
Convergence analysis of a weak Galerkin finite element method on a Shishkin mesh for a singularly perturbed fourth-order problem in 2D
Liu, Shicheng | Meng, Xiangyun | Zhai, QilongJournal of Computational and Applied Mathematics, Vol. 457 (2025), Iss. P.116324
https://doi.org/10.1016/j.cam.2024.116324 [Citations: 0] -
Alternating direction based method for optimal control problem constrained by Stokes equation
Gao, Yu | Li, Jingzhi | Song, Yongcun | Wang, Chao | Zhang, KaiJournal of Inverse and Ill-posed Problems, Vol. 30 (2022), Iss. 1 P.81
https://doi.org/10.1515/jiip-2020-0101 [Citations: 1] -
A novel variational method for 3D viscous flow in flow channel of turbomachines based on differential geometry
Ju, Guoliang | Li, Jingzhi | Li, KaitaiApplicable Analysis, Vol. 99 (2020), Iss. 13 P.2322
https://doi.org/10.1080/00036811.2018.1559304 [Citations: 1] -
Robust globally divergence-free Weak Galerkin finite element method for incompressible Magnetohydrodynamics flow
Zhang, Min | Zhang, Tong | Xie, XiaopingCommunications in Nonlinear Science and Numerical Simulation, Vol. 131 (2024), Iss. P.107810
https://doi.org/10.1016/j.cnsns.2023.107810 [Citations: 0] -
Analysis of Weak Galerkin Mixed Finite Element Method Based on the Velocity–Pseudostress Formulation for Navier–Stokes Equation on Polygonal Meshes
Gharibi, Zeinab | Dehghan, MehdiJournal of Scientific Computing, Vol. 101 (2024), Iss. 1
https://doi.org/10.1007/s10915-024-02651-w [Citations: 0] -
Numerical simulation for 3D flow in flow channel of aeroengine turbine fan based on dimension splitting method
Ju, Guoliang | Chen, Can | Chen, Rongliang | Li, Jingzhi | Li, Kaitai | Zhang, ShaohuiElectronic Research Archive, Vol. 28 (2020), Iss. 2 P.837
https://doi.org/10.3934/era.2020043 [Citations: 2] -
Constructing a CDG Finite Element with Order Two Superconvergence on Rectangular Meshes
Ye, Xiu | Zhang, ShangyouCommunications on Applied Mathematics and Computation, Vol. (2023), Iss.
https://doi.org/10.1007/s42967-023-00330-5 [Citations: 0] -
A time-explicit weak Galerkin scheme for parabolic equations on polytopal partitions
Wang, Junping | Ye, Xiu | Zhang, ShangyouJournal of Numerical Mathematics, Vol. 31 (2022), Iss. 2 P.125
https://doi.org/10.1515/jnma-2021-0128 [Citations: 2]