{"title":"A penalty method for approximation of the stationary Stokes–Darcy problem","authors":"","doi":"10.1016/j.cam.2024.116272","DOIUrl":null,"url":null,"abstract":"<div><p>In this work, the penalty method is studied for the mixed Stokes–Darcy problem, motivated by the penalty method applied to Stokes equation. This work first proposes the penalty Stokes–Darcy model at the continuous level. Then we prove that the solution of the penalty model converges strongly to the original solution as <span><math><mrow><mi>O</mi><mfenced><mrow><mi>ϵ</mi></mrow></mfenced></mrow></math></span> in which the penalty parameter is <span><math><mrow><mi>ϵ</mi><mo>→</mo><mn>0</mn></mrow></math></span>. What is more, the finite element method is used to solve the penalty model and the optimal error estimates are presented. Finally, several numerical tests are carried out to verify our theoretical results.</p></div>","PeriodicalId":50226,"journal":{"name":"Journal of Computational and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":2.1000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0377042724005211","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
In this work, the penalty method is studied for the mixed Stokes–Darcy problem, motivated by the penalty method applied to Stokes equation. This work first proposes the penalty Stokes–Darcy model at the continuous level. Then we prove that the solution of the penalty model converges strongly to the original solution as in which the penalty parameter is . What is more, the finite element method is used to solve the penalty model and the optimal error estimates are presented. Finally, several numerical tests are carried out to verify our theoretical results.
期刊介绍:
The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest.
The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.