奇异摄动问题不连续Galerkin法在层自适应网格上的一致收敛性分析

Q3 Multidisciplinary

Wuhan University Journal of Natural Sciences Pub Date : 2023-10-01 DOI:10.1051/wujns/2023285411

Jiamin SHI, Zhongshu LU, Luyi ZHANG, Sunjia LU, Yao CHENG

{"title":"奇异摄动问题不连续Galerkin法在层自适应网格上的一致收敛性分析","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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

摘要

本文研究一维奇异摄动问题的不连续伽辽金方法，该问题在经过简单变换后具有二阶对流扩散问题的基本特征。我们在一般框架下推导了八层自适应网格的DG方法的最优收敛性。收敛速度与小参数无关。此外，我们建立了一个更清晰的l2误差估计，如果真解有一个特殊的正则分量。并给出了数值实验结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Uniform Convergence Analysis of the Discontinuous Galerkin Method on Layer-Adapted Meshes for Singularly Perturbed Problem

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Wuhan University Journal of Natural Sciences Multidisciplinary-Multidisciplinary

CiteScore

0.40

自引率

0.00%

发文量

2485

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.