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Quadratic nonconforming finite element method for 3D Stokes equations on cuboid meshes

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Abstract

In this paper, the quadratic nonconforming brick element (MSLK element) introduced in [10] is used for the 3D Stokes equations. The instability for the mixed element pair MSLK−P 1 is analyzed, where the vector-valued MSLK element approximates the velocity and the piecewise P 1 element approximates the pressure. As a cure, we adopt the piecewise P 1 macroelement to discretize the pressure instead of the standard piecewise P 1 element on cuboid meshes. This new pair is stable and the optimal error estimate is achieved. Numerical examples verify our theoretical analysis.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Xin-chen Zhou, Zhao-liang Meng & Xiao-shan Wang

  2. School of Software, Dalian University of Technology, Dalian, 116024, China

    Zhong-xuan Luo

Authors
  1. Xin-chen Zhou
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  2. Zhao-liang Meng
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  3. Xiao-shan Wang
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  4. Zhong-xuan Luo
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Corresponding author

Correspondence to Xin-chen Zhou.

Additional information

Supported by the National Natural Science Foundation of China (11171052, 11301053, 61328206 and 61272371) and the Fundamental Research Funds for the Central Universities.

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Zhou, Xc., Meng, Zl., Wang, Xs. et al. Quadratic nonconforming finite element method for 3D Stokes equations on cuboid meshes. Appl. Math. J. Chin. Univ. 31, 21–36 (2016). https://doi.org/10.1007/s11766-016-3400-5

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  • DOI: https://doi.org/10.1007/s11766-016-3400-5

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