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A divergence-free weak Galerkin method for quasi-Newtonian Stokes flows

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Abstract

This paper proposes a weak Galerkin finite element method to solve incompressible quasi-Newtonian Stokes equations. We use piecewise polynomials of degrees k + 1 (k ≥ 0) and k for the velocity and pressure in the interior of elements, respectively, and piecewise polynomials of degrees k and k+1 for the boundary parts of the velocity and pressure, respectively. Wellposedness of the discrete scheme is established. The method yields a globally divergence-free velocity approximation. Optimal priori error estimates are derived for the velocity gradient and pressure approximations. Numerical results are provided to confirm the theoretical results.

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Acknowledgements

This work was supported by Major Research Plan of National Natural Science Foundation of China (Grant No. 91430105).

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Authors and Affiliations

  1. School of Mathematics, Sichuan University, Chengdu, 610064, China

    XiaoBo Zheng, Gang Chen & XiaoPing Xie

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  1. XiaoBo Zheng
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  2. Gang Chen
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  3. XiaoPing Xie
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Correspondence to XiaoPing Xie.

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Zheng, X., Chen, G. & Xie, X. A divergence-free weak Galerkin method for quasi-Newtonian Stokes flows. Sci. China Math. 60, 1515–1528 (2017). https://doi.org/10.1007/s11425-016-0354-8

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  • DOI: https://doi.org/10.1007/s11425-016-0354-8

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