{"title":"A Reynolds-semi-robust and pressure robust Hybrid High-Order method for the time dependent incompressible Navier--Stokes equations on general meshes","authors":"Daniel Castanon Quiroz, Daniele A. Di Pietro","doi":"arxiv-2409.07037","DOIUrl":null,"url":null,"abstract":"In this work we develop and analyze a Reynolds-semi-robust and\npressure-robust Hybrid High-Order (HHO) discretization of the incompressible\nNavier--Stokes equations. Reynolds-semi-robustness refers to the fact that,\nunder suitable regularity assumptions, the right-hand side of the velocity\nerror estimate does not depend on the inverse of the viscosity. This property\nis obtained here through a penalty term which involves a subtle projection of\nthe convective term on a subgrid space constructed element by element. The\nestimated convergence order for the $L^\\infty(L^2)$- and\n$L^2(\\text{energy})$-norm of the velocity is $h^{k+\\frac12}$, which matches the\nbest results for continuous and discontinuous Galerkin methods and corresponds\nto the one expected for HHO methods in convection-dominated regimes.\nTwo-dimensional numerical results on a variety of polygonal meshes complete the\nexposition.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
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.