An analysis of a weak Galerkin finite element method for stationary Navier-Stokes problems

作者：Zhang, Tie; Lin, Tao^*

来源：Journal of Computational and Applied Mathematics, 2019, 362: 484-497.

DOI：10.1016/j.cam.2018.07.037

• Weak Galerkin method
• Navier-Stokes equation
• Stability
• Discrete embedding inequality
• Optimal error estimate

In this article, we present and analyze a weak Galerkin finite element method for stationary Navier-Stokes problems. This weak Galerkin finite element scheme is based on a shape regular partition consisting of arbitrary polygons/polyhedra. We first establish a discrete embedding inequality that is useful in weak Galerkin finite element analysis for nonlinear problems. Then the stability and unique existence are proved for the discrete velocity and pressure by means of a discrete inf-sup condition. Furthermore, we derive the optimal error estimates for velocity approximation in the discrete H-1-norm and pressure approximation in the L-2-norm, respectively. Numerical examples are provided that corroborate the optimal convergence of the proposed method.

• 出版日期2019-12-15
• 单位东北大学; 美国弗吉尼亚理工大学(Virginia Tech)