A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations. Issue 5 (October 2014)

• Record Type: Journal Article
• Authors: Luo, Zhendong
• Is Part Of: Advances in applied mathematics and mechanics. Volume 6:Issue 5(2014)
• Page Start: 615
• Page End: 636
• Publication Date: 2014-10
• Subjects: 65N30, -- 65M30, -- 76M10; Non-stationary Navier-Stokes equations, -- finite volumes element method, -- error estimate, -- numerical simulations; Engineering mathematics -- Periodicals; Mechanics -- Periodicals; 620.00151825
• DOI: 10.4208/aamm.2013.m83
• Languages: English
• ISSNs: 2070-0733

Abstract

Abstract: A semi-discrete scheme about time for the non-stationary Navier-Stokes equations is presented firstly, then a new fully discrete finite volume element (FVE) formulation based on macroelement is directly established from the semi-discrete scheme about time. And the error estimates for the fully discrete FVE solutions are derived by means of the technique of the standard finite element method. It is shown by numerical experiments that the numerical results are consistent with theoretical conclusions. Moreover, it is shown that the FVE method is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes equations and it is one of the most effective numerical methods among the FVE formulation, the finite element formulation, and the finite difference scheme.