A stabilized finite volume method for the stationary Navier-Stokes equations

作者：Sheng, Ying; Zhang, Tie; Jiang, Zhong-Zhong^*

来源：Chaos Solitons & Fractals, 2016, 89: 363-372.

DOI：10.1016/j.chaos.2016.01.002

• Finite volume method
• Navier-Stokes problem
• Stabilized method
• P-1-P-0 element pair
• Inf-sup condition

In the present paper, we propose a stabilized finite volume element method for the Navier-Stokes equations using the lowest order P-1-P-0 element pair. The stabilized method is designed by adding a jump term of the discrete pressure to the continuity approximation equation. A discrete inf-sup condition is established for the stabilized finite volume element scheme which assures the stability of the discrete solutions. The optimal error estimates are derived in the H-1-norm for velocity and the L-2-norm for pressure, respectively. Moreover, the optimal L-2- error estimate is also given for velocity approximation.

• 出版日期2016-8
• 单位东北大学