Optimal [math] Error Analysis of a Loosely Coupled Finite Element Scheme for Thin-Structure Interactions

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2024-07-30 DOI:10.1137/23m1578401

Buyang Li, Weiwei Sun, Yupei Xie, Wenshan Yu

{"title":"Optimal [math] Error Analysis of a Loosely Coupled Finite Element Scheme for Thin-Structure Interactions","authors":"Buyang Li, Weiwei Sun, Yupei Xie, Wenshan Yu","doi":"10.1137/23m1578401","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1782-1813, August 2024. <br/> Abstract. Finite element methods and kinematically coupled schemes that decouple the fluid velocity and structure displacement have been extensively studied for incompressible fluid-structure interactions (FSIs) over the past decade. While these methods are known to be stable and easy to implement, optimal error analysis has remained challenging. Previous work has primarily relied on the classical elliptic projection technique, which is only suitable for parabolic problems and does not lead to optimal convergence of numerical solutions for the FSI problems in the standard [math] norm. In this article, we propose a new stable fully discrete kinematically coupled scheme for the incompressible FSI thin-structure model and establish a new approach for the numerical analysis of FSI problems in terms of a newly introduced coupled nonstationary Ritz projection, which allows us to prove the optimal-order convergence of the proposed method in the [math] norm. The methodology presented in this article is also applicable to numerous other FSI models and serves as a fundamental tool for advancing research in this field.","PeriodicalId":49527,"journal":{"name":"SIAM Journal on Numerical Analysis","volume":"74 1","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2024-07-30","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/10.1137/23m1578401","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

Abstract

SIAM Journal on Numerical Analysis, Volume 62, Issue 4, Page 1782-1813, August 2024.
Abstract. Finite element methods and kinematically coupled schemes that decouple the fluid velocity and structure displacement have been extensively studied for incompressible fluid-structure interactions (FSIs) over the past decade. While these methods are known to be stable and easy to implement, optimal error analysis has remained challenging. Previous work has primarily relied on the classical elliptic projection technique, which is only suitable for parabolic problems and does not lead to optimal convergence of numerical solutions for the FSI problems in the standard [math] norm. In this article, we propose a new stable fully discrete kinematically coupled scheme for the incompressible FSI thin-structure model and establish a new approach for the numerical analysis of FSI problems in terms of a newly introduced coupled nonstationary Ritz projection, which allows us to prove the optimal-order convergence of the proposed method in the [math] norm. The methodology presented in this article is also applicable to numerous other FSI models and serves as a fundamental tool for advancing research in this field.

查看原文本刊更多论文

针对薄结构相互作用的松耦合有限元方案的最优[数学]误差分析

SIAM 数值分析期刊》第 62 卷第 4 期第 1782-1813 页，2024 年 8 月。摘要。在过去十年中，针对不可压缩流固耦合（FSI）问题，人们广泛研究了有限元方法和运动耦合方案，这些方法将流体速度和结构位移解耦。众所周知，这些方法既稳定又易于实施，但最佳误差分析仍具有挑战性。以往的工作主要依赖于经典的椭圆投影技术，该技术只适用于抛物线问题，并不能使 FSI 问题的数值解在标准[数学]规范下达到最佳收敛。在本文中，我们针对不可压缩 FSI 薄结构模型提出了一种新的稳定的全离散运动耦合方案，并从新引入的耦合非稳态 Ritz 投影角度建立了 FSI 问题数值分析的新方法，从而证明了所提方法在[math]规范下的最优阶收敛性。本文提出的方法也适用于许多其他 FSI 模型，是推进该领域研究的基础工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.