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Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem

Juan Wen (School of Sciences, Xi’an University of Technology, Xi’an, China)
Yinnian He (Department of Mathematics, Xi’an Jiaotong University, Xi’an, China)
Xin Zhao (Department of Mathematics and Geographical Science and Environment Engineering, Baoji University of Arts and Sciences, Xi’an, China)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 7 November 2016

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 P1/P1.

Findings

The stability and convergence of the optimal order in H1-norm for velocity and L2-norm for pressure are obtained.

Originality/value

Using a dual problem for the Navier-Stokes problem, the convergence of the optimal order in L2-norm for the velocity is obtained. Finally, numerical example confirms the theory analysis and validates the effectiveness of this new method.

Keywords

Acknowledgements

This work are supported by the special research program of the Education Department of Shaanxi Province (No. 16JK1537), the NSF of China (Nos 11271298, 11571275).

Citation

Wen, J., He, Y. and Zhao, X. (2016), "Analysis of a new stabilized finite volume element method based on multiscale enrichment for the Navier-Stokes problem", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 26 No. 8, pp. 2462-2485. https://doi.org/10.1108/HFF-06-2015-0244

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Publisher

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Emerald Group Publishing Limited

Copyright © 2016, Emerald Group Publishing Limited

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