耦合对流-扩散-反应问题的Darcy-Forchheimer问题的有限元方法

IF 1.9 3区数学 Q2 Mathematics

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique Pub Date : 2021-10-07 DOI:10.1051/m2an/2021066

Toni Sayah, G. Semaan, Faouzi Triki

{"title":"耦合对流-扩散-反应问题的Darcy-Forchheimer问题的有限元方法","authors":"Toni Sayah, G. Semaan, Faouzi Triki","doi":"10.1051/m2an/2021066","DOIUrl":null,"url":null,"abstract":"In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm the theoretical accuracy of the discretization.","PeriodicalId":50499,"journal":{"name":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","volume":"73 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2021-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem\",\"authors\":\"Toni Sayah, G. Semaan, Faouzi Triki\",\"doi\":\"10.1051/m2an/2021066\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm the theoretical accuracy of the discretization.\",\"PeriodicalId\":50499,\"journal\":{\"name\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"volume\":\"73 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2021-10-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/m2an/2021066\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/m2an/2021066","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 2

摘要

在本文中，我们考虑了一个依赖于浓度的非线性外力耦合的对流-扩散-反应问题- Darcy-Forchheimer问题。利用伽辽金方法建立了解的存在性，并证明了解的唯一性。介绍并分析了一种基于有限元法的数值方案。然后对每一种数值格式导出最优先验误差估计。通过数值计算验证了离散化的理论精度。

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

Finite element methods for the Darcy-Forchheimer problem coupled with the convection-diffusion-reaction problem

In this article, we consider the convection-diffusion-reaction problem coupled the Darcy-Forchheimer problem by a non-linear external force depending on the concentration. We establish existence of a solution by using a Galerkin method and we prove uniqueness. We introduce and analyse a numerical scheme based on the finite element method. An optimal a priori error estimate is then derived for each numerical scheme. Numerical investigation are performed to confirm the theoretical accuracy of the discretization.

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

Esaim-Mathematical Modelling and Numerical Analysis-Modelisation Mathematique et Analyse Numerique 数学-应用数学

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

6-12 weeks

期刊介绍： M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.