线性化磁流体力学的稳健有限元

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-07-09 DOI:10.1137/23m1582783

L. Beirão da Veiga, F. Dassi, G. Vacca

{"title":"线性化磁流体力学的稳健有限元","authors":"L. Beirão da Veiga, F. Dassi, G. Vacca","doi":"10.1137/23m1582783","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1539-1564, August 2024. <br/> Abstract. We introduce a pressure robust finite element method for the linearized magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a nonconforming BDM approach with suitable DG terms for the fluid part, combined with an [math]-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"54 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Robust Finite Elements for Linearized Magnetohydrodynamics\",\"authors\":\"L. Beirão da Veiga, F. Dassi, G. Vacca\",\"doi\":\"10.1137/23m1582783\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1539-1564, August 2024. <br/> Abstract. We introduce a pressure robust finite element method for the linearized magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a nonconforming BDM approach with suitable DG terms for the fluid part, combined with an [math]-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments.\",\"PeriodicalId\":49527,\"journal\":{\"name\":\"SIAM Journal on Numerical Analysis\",\"volume\":\"54 1\",\"pages\":\"\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Numerical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1582783\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Numerical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1582783","RegionNum":2,"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

摘要

SIAM 数值分析期刊》第 62 卷第 4 期第 1539-1564 页，2024 年 8 月。摘要。我们介绍了一种三维空间线性化磁流体动力学方程的压力稳健有限元方法，该方法在存在高流体和磁场雷诺数的情况下也能证明是准稳健的。所提出的方案采用了一种非顺应性 BDM 方法，流体部分采用了合适的 DG 项，磁通量采用了[math]顺应性选择。该方法还引入了与耦合项相关的特定 CIP 型稳定。最后，数值实验进一步验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Robust Finite Elements for Linearized Magnetohydrodynamics

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1539-1564, August 2024.
Abstract. We introduce a pressure robust finite element method for the linearized magnetohydrodynamics equations in three space dimensions, which is provably quasi-robust also in the presence of high fluid and magnetic Reynolds numbers. The proposed scheme uses a nonconforming BDM approach with suitable DG terms for the fluid part, combined with an [math]-conforming choice for the magnetic fluxes. The method introduces also a specific CIP-type stabilization associated to the coupling terms. Finally, the theoretical result are further validated by numerical experiments.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.