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A Posteriori Error Analysis for Pressure-Robust HDG Methods for the Stationary Incompressible Navier–Stokes Equations

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Abstract

A hybridizable discontinuous Galerkin method with divergence-free and H(div)-conforming velocity field is considered in this paper for the stationary incompressible Navier–Stokes equations. The pressure-robustness, which means that a priori error estimates for the velocity is independent of the pressure error, is satisfied. As a consequence, an efficient and reliable a posteriori error estimator is proved for the \(L^2\)-errors in the velocity gradient and pressure under a smallness assumption. We conclude by several numerical examples which reveal the pressure-robustness and show the performance of the obtained a posteriori error estimator.

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Funding

The work was supported by the NSF of China (Grant No. 12001209).

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  1. School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510000, Guangdong, China

    Haitao Leng

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  1. Haitao Leng
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Leng, H. A Posteriori Error Analysis for Pressure-Robust HDG Methods for the Stationary Incompressible Navier–Stokes Equations. J Sci Comput 94, 52 (2023). https://doi.org/10.1007/s10915-023-02104-w

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