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A New Finite Volume Element Formulation for the Non-Stationary Navier-Stokes Equations

Published online by Cambridge University Press:  03 June 2015

Zhendong Luo
Zhendong Luo*
Affiliation:
School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China
*
*Corresponding author. Email: zhdluo@ncepu.edu.cn
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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.

Keywords

65N3065M3076M10Non-stationary Navier-Stokes equationsfinite volumes element methoderror estimatenumerical simulations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 6 , Issue 5 , October 2014 , pp. 615 - 636
Copyright
Copyright © Global-Science Press 2014

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