{"title":"二维抛物对流扩散问题奇摄动系统的鲁棒计算方法","authors":"M. K. Singh, S. Natesan","doi":"10.1504/IJMMNO.2019.10018804","DOIUrl":null,"url":null,"abstract":"This article presents a numerical scheme to solve singularly perturbed system of 2D parabolic convection-diffusion problem exhibiting exponential boundary layers. The numerical scheme consists of a fractional implicit-Euler scheme on uniform mesh for time discretisation and the classical upwind scheme on a piecewise uniform Shishkin mesh for spatial discretisation. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimates are derived. It is shown that the numerical scheme is uniformly convergent with respect to the singular perturbation parameter. The proposed method is applied to a test problem to verify theoretical results numerically.","PeriodicalId":13553,"journal":{"name":"Int. J. Math. Model. Numer. Optimisation","volume":"38 1","pages":"127-157"},"PeriodicalIF":0.0000,"publicationDate":"2019-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"A robust computational method for singularly perturbed system of 2D parabolic convection-diffusion problems\",\"authors\":\"M. K. Singh, S. Natesan\",\"doi\":\"10.1504/IJMMNO.2019.10018804\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article presents a numerical scheme to solve singularly perturbed system of 2D parabolic convection-diffusion problem exhibiting exponential boundary layers. The numerical scheme consists of a fractional implicit-Euler scheme on uniform mesh for time discretisation and the classical upwind scheme on a piecewise uniform Shishkin mesh for spatial discretisation. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimates are derived. It is shown that the numerical scheme is uniformly convergent with respect to the singular perturbation parameter. The proposed method is applied to a test problem to verify theoretical results numerically.\",\"PeriodicalId\":13553,\"journal\":{\"name\":\"Int. J. Math. Model. Numer. Optimisation\",\"volume\":\"38 1\",\"pages\":\"127-157\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-01-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Math. Model. Numer. Optimisation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1504/IJMMNO.2019.10018804\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Math. Model. Numer. Optimisation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1504/IJMMNO.2019.10018804","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A robust computational method for singularly perturbed system of 2D parabolic convection-diffusion problems
This article presents a numerical scheme to solve singularly perturbed system of 2D parabolic convection-diffusion problem exhibiting exponential boundary layers. The numerical scheme consists of a fractional implicit-Euler scheme on uniform mesh for time discretisation and the classical upwind scheme on a piecewise uniform Shishkin mesh for spatial discretisation. For the proposed scheme, the stability analysis is presented and parameter-uniform error estimates are derived. It is shown that the numerical scheme is uniformly convergent with respect to the singular perturbation parameter. The proposed method is applied to a test problem to verify theoretical results numerically.