Multiscale enrichment of a finite volume element method for the stationary Navier–Stokes problem

Abstract

In this paper, we introduce a finite volume element method for the Navier–Stokes problem. This method is based on the multiscale enrichment and uses the lowest finite element pair P ₁/P ₀. The stability and convergence of the optimal order in H ¹-norm for velocity and L ²-norm for pressure are obtained. Using a dual problem for the Navier–Stokes problem, we establish the convergence of the optimal order in L ²-norm for the velocity.

Keywords:

• finite volume element method
• P ₁/P ₀ elements
• multiscale enrichment
• the Navier–Stokes problem

2000 AMS Subject Classifications :

• 35Q10
• 65N30
• 76D05

Acknowledgements

We thank the anonymous referees for their careful reading of the manuscript and suggestions that greatly help to improve the paper. This work is supported by the NSF of China (No. 11271298).