{"title":"Superconvergence analysis of the bilinear‐constant scheme for two‐dimensional incompressible convective Brinkman–Forchheimer equations","authors":"Huaijun Yang, Xu Jia","doi":"10.1002/num.23060","DOIUrl":null,"url":null,"abstract":"In this article, a low order conforming mixed finite element method is proposed and investigated for two‐dimensional convective Brinkman–Forchheimer equations. Based on the special properties of the bilinear‐constant finite element pair on the rectangular mesh and the careful treatment of the nonlinear terms, the superclose error estimates for velocity in H1$$ {H}^1 $$ ‐norm and pressure in L2$$ {L}^2 $$ ‐norm are obtained. Then, in terms of interpolation post‐processing technique, the global superconvergence results are derived. Finally, some numerical experiments are carried out to demonstrate the correctness of the theoretical findings.","PeriodicalId":19443,"journal":{"name":"Numerical Methods for Partial Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2023-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Methods for Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1002/num.23060","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, a low order conforming mixed finite element method is proposed and investigated for two‐dimensional convective Brinkman–Forchheimer equations. Based on the special properties of the bilinear‐constant finite element pair on the rectangular mesh and the careful treatment of the nonlinear terms, the superclose error estimates for velocity in H1$$ {H}^1 $$ ‐norm and pressure in L2$$ {L}^2 $$ ‐norm are obtained. Then, in terms of interpolation post‐processing technique, the global superconvergence results are derived. Finally, some numerical experiments are carried out to demonstrate the correctness of the theoretical findings.
期刊介绍：
An international journal that aims to cover research into the development and analysis of new methods for the numerical solution of partial differential equations, it is intended that it be readily readable by and directed to a broad spectrum of researchers into numerical methods for partial differential equations throughout science and engineering. The numerical methods and techniques themselves are emphasized rather than the specific applications. The Journal seeks to be interdisciplinary, while retaining the common thread of applied numerical analysis.
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