{"title":"用于一般网格上时变不可压缩纳维-斯托克斯方程的雷诺稳态和压力稳健混合高阶方法","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":"{\"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}","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}
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.