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An efficient two-step algorithm for the incompressible flow problem

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An Erratum to this article was published on 12 July 2016

Abstract

A new two-step stabilized finite element method for the 2D/3D stationary Navier–Stokes equations based on local Gauss integration is introduced and analyzed in this paper. The method consists of solving one Navier–Stokes problem based on the P 1−P 1 finite element pair and then solving a general Stokes problem based on the P 2−P 2 finite element pair, i.e., computes a lower order predictor and a higher order corrector. Moreover, the stability and convergence of the present method are deduced, which show that the new method provides an approximate solution with the convergence rate of the same order as the P 2−P 2 stabilized finite element solution solving the Navier–Stokes equations on the same mesh width. However, our method can save a large amount of computational time. Finally, numerical tests confirm the theoretical results of the method.

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Authors and Affiliations

  1. College of Mathematics and System Sciences, Xinjiang University, Urumqi, 830046, People’s Republic of China

    Pengzhan Huang, Xinlong Feng & Yinnian He

  2. Center for Computational Geosciences, School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Yinnian He

Authors
  1. Pengzhan Huang
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  2. Xinlong Feng
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  3. Yinnian He
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Correspondence to Pengzhan Huang.

Additional information

Communicated by: A. Zhou

This research was supported by the NSF of China (Grant No. 11401511), the Distinguished Young Scholars Fund of Xinjiang Province (Grant No. 2013711010), the China Postdoctoral Science Foundation (Grant No. 2014T70954) and the Scientific Research Program of the Higher Education Institution of Xinjiang (Grant No. XJEDU2014S002).

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Huang, P., Feng, X. & He, Y. An efficient two-step algorithm for the incompressible flow problem. Adv Comput Math 41, 1059–1077 (2015). https://doi.org/10.1007/s10444-014-9400-1

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  • DOI: https://doi.org/10.1007/s10444-014-9400-1

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