{"title":"Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems","authors":"Aayushman Raina, Srinivasan Natesan, Şuayip Toprakseven","doi":"arxiv-2409.07217","DOIUrl":null,"url":null,"abstract":"We consider the Weak Galerkin finite element approximation of the Singularly\nPerturbed Biharmonic elliptic problem on a unit square domain with clamped\nboundary conditions. Shishkin mesh is used for domain discretization as the\nsolution exhibits boundary layers near the domain boundary. Error estimates in\nthe equivalent $H^{2}-$ norm have been established and the uniform convergence\nof the proposed method has been proved. Numerical examples are presented\ncorroborating our theoretical findings.","PeriodicalId":501162,"journal":{"name":"arXiv - MATH - Numerical Analysis","volume":"32 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.07217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the Weak Galerkin finite element approximation of the Singularly
Perturbed Biharmonic elliptic problem on a unit square domain with clamped
boundary conditions. Shishkin mesh is used for domain discretization as the
solution exhibits boundary layers near the domain boundary. Error estimates in
the equivalent $H^{2}-$ norm have been established and the uniform convergence
of the proposed method has been proved. Numerical examples are presented
corroborating our theoretical findings.
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