共轭亥姆霍兹方程全通量公式的HDG解的构造和分析

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Mathematics of Computation Pub Date : 2023-05-04 DOI:10.1090/mcom/3850

Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux

{"title":"共轭亥姆霍兹方程全通量公式的HDG解的构造和分析","authors":"Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux","doi":"10.1090/mcom/3850","DOIUrl":null,"url":null,"abstract":"We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.","PeriodicalId":18456,"journal":{"name":"Mathematics of Computation","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation\",\"authors\":\"Hélène Barucq, Nathan Rouxelin, Sébastien Tordeux\",\"doi\":\"10.1090/mcom/3850\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.\",\"PeriodicalId\":18456,\"journal\":{\"name\":\"Mathematics of Computation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mcom/3850\",\"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":"Mathematics of Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mcom/3850","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: 1

摘要

基于总通量公式，引入了一种求解共轭亥姆霍兹方程的杂交不连续伽辽金(HDG)方法，其中未知向量同时表示扩散和对流现象。这种HDG方法对所有未知数具有相同的插值度，并计算出惩罚参数的物理通知值。详细分析了该方法的局部适定性和全局适定性，并给出了超收敛结果。然后，我们提供数值实验来说明理论结果。

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

Construction and analysis of a HDG solution for the total-flux formulation of the convected Helmholtz equation

We introduce a hybridizable discontinuous Galerkin (HDG) method for the convected Helmholtz equation based on the total flux formulation, in which the vector unknown represents both diffusive and convective phenomena. This HDG method is constricted with the same interpolation degree for all the unknowns and a physically informed value for the penalization parameter is computed. A detailed analysis including local and global well-posedness as well as a super-convergence result is carried out. We then provide numerical experiments to illustrate the theoretical results.

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

Mathematics of Computation 数学-应用数学

CiteScore

3.90

自引率

5.00%

发文量

审稿时长

7.0 months

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in computational mathematics. Areas covered include numerical analysis, computational discrete mathematics, including number theory, algebra and combinatorics, and related fields such as stochastic numerical methods. Articles must be of significant computational interest and contain original and substantial mathematical analysis or development of computational methodology.