Analysis of newton multilevel stabilized finite volume method for the three-dimensional stationary Navier-Stokes equations

Authors

  • Xin Zhao,

    1. Department of Mathematics and Geographical Science and Environment Engineering, Baoji University of Arts and Sciences, Baoji, 721007, People's Republic of China
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  • Jian Li,

    Corresponding author
    1. Department of Mathematics and Geographical Science and Environment Engineering, Baoji University of Arts and Sciences, Baoji, 721007, People's Republic of China
    2. Center for Computational Geoscience, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
    • Department of Mathematics and Geographical Science and Environment Engineering, Baoji University of Arts and Sciences, Baoji, 721007, People's Republic of China
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  • Jian Su,

    Corresponding author
    1. Center for Computational Geoscience, School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, People's Republic of China
    • School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, P.R. China
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  • Gang Lei

    1. Department of Mathematics and Geographical Science and Environment Engineering, Baoji University of Arts and Sciences, Baoji, 721007, People's Republic of China
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Abstract

This article proposes and analyzes a multilevel stabilized finite volume method(FVM) for the three-dimensional stationary Navier–Stokes equations approximated by the lowest equal-order finite element pairs. The method combines the new stabilized FVM with the multilevel discretization under the assumption of the uniqueness condition. The multilevel stabilized FVM consists of solving the nonlinear problem on the coarsest mesh and then performs one Newton correction step on each subsequent mesh thus only solving one large linear systems. The error analysis shows that the multilevel-stabilized FVM provides an approximate solution with the convergence rate of the same order as the usual stabilized finite element solution solving the stationary Navier–Stokes equations on a fine mesh for an appropriate choice of mesh widths: hjhj-12, j = 1,…,J. Therefore, the multilevel stabilized FVM is more efficient than the standard one-level-stabilized FVM. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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