Jiamin SHI, Zhongshu LU, Luyi ZHANG, Sunjia LU, Yao CHENG
{"title":"Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem","authors":"Jiamin SHI, Zhongshu LU, Luyi ZHANG, Sunjia LU, Yao CHENG","doi":"10.1051/wujns/2023285411","DOIUrl":null,"url":null,"abstract":"This paper concerns a discontinuous Galerkin (DG) method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations. We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework. The convergence rate is valid independent of the small parameter. Furthermore, we establish a sharper L 2 -error estimate if the true solution has a special regular component. Numerical experiments are also given.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":"51 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wuhan University Journal of Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/wujns/2023285411","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
引用次数: 0
Abstract
This paper concerns a discontinuous Galerkin (DG) method for a one-dimensional singularly perturbed problem which possesses essential characteristic of second order convection-diffusion problem after some simple transformations. We derive an optimal convergence of the DG method for eight layer-adapted meshes in a general framework. The convergence rate is valid independent of the small parameter. Furthermore, we establish a sharper L 2 -error estimate if the true solution has a special regular component. Numerical experiments are also given.
期刊介绍:
Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.