{"title":"A high-order conservative cut finite element method for problems in time-dependent domains","authors":"","doi":"10.1016/j.cma.2024.117245","DOIUrl":null,"url":null,"abstract":"<div><p>A mass-conservative high-order unfitted finite element method for convection–diffusion equations in evolving domains is proposed. The space–time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynolds’ transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered.</p></div>","PeriodicalId":55222,"journal":{"name":"Computer Methods in Applied Mechanics and Engineering","volume":null,"pages":null},"PeriodicalIF":6.9000,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045782524005012/pdfft?md5=de1393038de8878ba19b25d3560862e5&pid=1-s2.0-S0045782524005012-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Applied Mechanics and Engineering","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0045782524005012","RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
A mass-conservative high-order unfitted finite element method for convection–diffusion equations in evolving domains is proposed. The space–time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynolds’ transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered.
针对演化域中的对流扩散方程，提出了一种质量守恒高阶非拟合有限元方法。P. Hansbo, M. G. Larson, S. Zahedi, Comput.Hansbo, M. G. Larson, S. Zahedi, Comput.Methods Appl.Engrg.307 (2016)] 中提出的时空方法进行了扩展，利用雷诺输运定理自然实现了质量守恒。此外，通过将随时间变化的域划分为宏元，为随时间变化的域中的切割有限元法提出了一种更有效的稳定程序。数值实验表明，该方法能满足质量守恒要求，实现高阶收敛，并在增加稀疏性的同时控制了系统矩阵的条件数。研究考虑了体域问题以及体-面耦合问题。
期刊介绍：
Computer Methods in Applied Mechanics and Engineering stands as a cornerstone in the realm of computational science and engineering. With a history spanning over five decades, the journal has been a key platform for disseminating papers on advanced mathematical modeling and numerical solutions. Interdisciplinary in nature, these contributions encompass mechanics, mathematics, computer science, and various scientific disciplines. The journal welcomes a broad range of computational methods addressing the simulation, analysis, and design of complex physical problems, making it a vital resource for researchers in the field.
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