{"title":"Variational Approximation in Modular Spaces by Using Finite Element Method Approach","authors":"M. Mabdaoui, H. Moussa, M. Rhoudaf","doi":"10.1080/01630563.2022.2153367","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea’s Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2022-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/01630563.2022.2153367","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
Abstract In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea’s Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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