{"title":"Approximation and optimal control for variational–hemivariational inequalities of Bingham type fluid","authors":"Zakaria Faiz, Hicham Benaissa","doi":"10.1007/s40314-024-02787-3","DOIUrl":null,"url":null,"abstract":"<p>The aim of this paper is to investigate a model of incompressible fluid of Bingham type in a bounded domain. We obtain the variational formulation of the model of incompressible fluid which is a variational–hemivariational inequality. The existence and uniqueness of the solution are proven utilizing recent advancements in the theory of hemivariational inequalities. Additionally, employing the finite element method, we analyze a fully discrete approximation of the model and provide error estimates for the approximate solutions. Finally, we demonstrate a continuous dependence result and establish the existence of optimal pairs for the incompressible fluid of Bingham type.</p>","PeriodicalId":51278,"journal":{"name":"Computational and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s40314-024-02787-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this paper is to investigate a model of incompressible fluid of Bingham type in a bounded domain. We obtain the variational formulation of the model of incompressible fluid which is a variational–hemivariational inequality. The existence and uniqueness of the solution are proven utilizing recent advancements in the theory of hemivariational inequalities. Additionally, employing the finite element method, we analyze a fully discrete approximation of the model and provide error estimates for the approximate solutions. Finally, we demonstrate a continuous dependence result and establish the existence of optimal pairs for the incompressible fluid of Bingham type.
期刊介绍：
Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics).
The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.
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