A Stabilized Low Order Finite-Volume Method for the Three-Dimensional Stationary Navier-Stokes Equations. (14th February 2012)

• Record Type: Journal Article
• Authors: Li, Jian; Zhao, Xin; Wu, Jianhua; Yang, Jianhong
• Other Names: Martinez-Guerra Rafael Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2012(2012)
• Publication Date: 2012-02-14
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2012/297269
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper proposes and analyzes a stabilized finite-volume method (FVM) for the three-dimensional stationary Navier-Stokes equations approximated by the lowest order finite element pairs. The method studies the new stabilized FVM with the relationship between the stabilized FEM (FEM) and the stabilized FVM under the assumption of the uniqueness condition. The results have three prominent features in this paper. Firstly, the error analysis shows that the stabilized FVM provides an approximate solution with the optimal convergence rate of the same order as the usual stabilized FEM solution solving the stationary Navier-Stokes equations. Secondly, superconvergence results on the solutions of the stabilized FEM and stabilized FVM are derived on the H 1 -norm and the L 2 -norm for the velocity and pressure. Thirdly, residual technique is applied to obtain the L 2 -norm error for the velocity without additional regular assumption on the exact solution.