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A Posteriori Error Analysis of the Hybrid High-Order Method for the Stokes Problem

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Abstract

We present a residual-based a posteriori error estimator for the Hybrid High-Order (HHO) method for the Stokes model problem. Both the proposed HHO method and error estimator are valid in two and three dimensions and support arbitrary approximation orders on fairly general meshes. The upper bound and lower bound of the error estimator are proved, in which proof, the key ingredient is a novel stabilizer employed in the discrete scheme. By using the given estimator, adaptive algorithm of HHO method is designed to solve model problem. Finally, the expected theoretical results are numerically demonstrated on a variety of meshes for model problem.

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Acknowledgements

The authors should thank Huayi Wei from Xiangtan University, China, for the valuable discussions of the codes in FEALPy. The work is partially supported by the NSF of China (Nos. 12001433 and 12101495) and General Special Project of Education Department of Shaanxi Provincial Government (No. 21JK0943).

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710069, Shaanxi, People’s Republic of China

    Yongchao Zhang

  2. School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, 710049, Shaanxi, People’s Republic of China

    Liquan Mei

  3. School of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an, 710062, Shaanxi, People’s Republic of China

    Gang Wang

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  1. Yongchao Zhang
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Correspondence to Gang Wang.

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Zhang, Y., Mei, L. & Wang, G. A Posteriori Error Analysis of the Hybrid High-Order Method for the Stokes Problem. J Sci Comput 96, 74 (2023). https://doi.org/10.1007/s10915-023-02291-6

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