Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem. Issue 8 (7th November 2016)

• Record Type: Journal Article
• Authors: Wen, Juan; He, Yinnian; Zhao, Xin
• Is Part Of: International journal of numerical methods for heat & fluid flow. Volume 26:Issue 8(2016)
• Page Start: 2462
• Page End: 2485
• Publication Date: 2016-11-07
• Subjects: P1/P1 elements -- Finite volume element method -- Multiscale enrichment -- The Navier-Stokes equations; Heat -- Transmission -- Mathematics -- Periodicals; Fluid dynamics -- Mathematics -- Periodicals; 536.2
• DOI: 10.1108/HFF-06-2015-0244
• Languages: English
• ISSNs: 0961-5539

Abstract

Abstract : Purpose: The purpose of this paper is to propose a new stabilized finite volume element method for the Navier-Stokes problem. Design/methodology/approach: This new method is based on the multiscale enrichment and uses the lowest equal order finite element pairs P 1 / P 1 . Findings: The stability and convergence of the optimal order in H 1 -norm for velocity and L 2 -norm for pressure are obtained. Originality/value: Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L 2 -norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.