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Improved parallel finite element methods for the stationary Navier–Stokes problem

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Abstract

In this study, two improved parallel finite element algorithms based on two-grid strategies are developed to approximate the stationary Navier–Stokes equations. Algorithms are devised to improve the existing local and parallel finite element methods to arrive at \(L^2\) optimal velocity approximation by considering one further coarse grid correction. Rigorously numerical analysis is established, and numerical experiments are reported to support the theoretical findings.

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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 (Nos. 12172202, 12001234), the Support Plan for Outstanding Youth Innovation Team in Shandong Higher Education Institutions (No. 2022KJ249), and the Natural Science Foundation of Shandong Province (No. ZR2021MA063).

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Authors and Affiliations

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

    Guangzhi Du

  2. School of Mathematical Sciences, University of Jinan, Jinan, 250022, China

    Liyun Zuo

Authors
  1. Guangzhi Du
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  2. Liyun Zuo
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Contributions

GD: formal analysis, visualization, writing, review. LZ: conceptualization, methodology, validation, review. All authors reviewed the manuscript.

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Correspondence to Liyun Zuo.

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Du, G., Zuo, L. Improved parallel finite element methods for the stationary Navier–Stokes problem. Numer Algor 97, 1383–1396 (2024). https://doi.org/10.1007/s11075-024-01754-7

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  • DOI: https://doi.org/10.1007/s11075-024-01754-7

Keywords

Mathematics Subject Classification (2010)