A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes
<|reference_start|>A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes: In this work we develop and analyze a Reynolds-semi-robust and pressure-robust Hybrid High-Order (HHO) discretization of the incompressible Navier--Stokes equations. Reynolds-semi-robustness refers to the fact that, under suitable regularity assumptions, the right-hand side of the velocity error estimate does not depend on the inverse of the viscosity. This property is obtained here through a penalty term which involves a subtle projection of the convective term on a subgrid space constructed element by element. The estimated convergence order for the $L^\infty(L^2)$- and $L^2(\text{energy})$-norm of the velocity is $h^{k+\frac12}$, which matches the best results for continuous and discontinuous Galerkin methods and corresponds to the one expected for HHO methods in convection-dominated regimes. Two-dimensional numerical results on a variety of polygonal meshes complete the exposition.<|reference_end|>
@article{quiroz2024a,
    title={A Reynolds-semi-robust and pressure robust Hybrid High-Order method for
  the time dependent incompressible Navier--Stokes equations on general meshes},
    author={Daniel Castanon Quiroz and Daniele A. Di Pietro},
    journal={arXiv preprint arXiv:2409.07037},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07037},
    primaryClass={math.NA cs.NA}
}