{"title":"Local discontinuous Galerkin method on graded meshes for a third‐order singularly perturbed problem","authors":"Li Yan, Yao Cheng","doi":"10.1002/zamm.202300238","DOIUrl":null,"url":null,"abstract":"We consider the local discontinuous Galerkin (LDG) method for a third order singularly perturbed problem with different kinds of boundary layer. On graded Duran‐Shishkin and Duran type meshes, we prove optimal order error estimate in the energy‐norm which is valid uniformly up to a logarithmic factor. Numerical experiments are given to confirm our theoretical findings.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":"167 1","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2023-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202300238","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
We consider the local discontinuous Galerkin (LDG) method for a third order singularly perturbed problem with different kinds of boundary layer. On graded Duran‐Shishkin and Duran type meshes, we prove optimal order error estimate in the energy‐norm which is valid uniformly up to a logarithmic factor. Numerical experiments are given to confirm our theoretical findings.
期刊介绍：
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.
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