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Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations

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Abstract

Based on two-grid discretizations, some local and parallel stabilized finite element methods are proposed and investigated for the Stokes problem in this paper. For the finite element discretization, the lowest equal-order finite element pairs are chosen to circumvent the discrete inf-sup condition. In these algorithms, we derive the low-frequency components of the solution for the Stokes problem on a coarse grid and catch the high-frequency components on a fine grid using some local and parallel procedures. Optimal error bounds are demonstrated and some numerical experiments are carried out to support theoretical results.

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Acknowledgements

The authors would like to thank the reviewers for their constructive comments, which allowed for the improvement of the presentation of the results.

Funding

This work is subsidized by the National Natural Science Foundation of China (No. 12172202), the Natural Science Foundation of Shandong Province (No. ZR2021MA063), the Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions (No. 2021KJ037), the Natural Science Foundation of Shaanxi Province (No. 2021JQ-426), and the Scientific Research Program of Shaanxi Provincial Education Department (No. 21JK0935).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, China

    Xinhui Wang & Guangzhi Du

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  1. Xinhui Wang
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  2. Guangzhi Du
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Xinhui Wang: formal analysis, visualization, writing, review. Guangzhi Du: conceptualization, methodology, validation, review. All authors reviewed the manuscript.

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Correspondence to Guangzhi Du.

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Wang, X., Du, G. Local and parallel stabilized finite element methods based on two-grid discretizations for the Stokes equations. Numer Algor 93, 67–83 (2023). https://doi.org/10.1007/s11075-022-01403-x

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