{"title":"具有齐次跳跃条件的非线性双曲型方程的近似解","authors":"M. O. Adewole","doi":"10.33993/jnaat482-1175","DOIUrl":null,"url":null,"abstract":"We present the error analysis of class of second order nonlinear hyperbolic interface problem where the spatial and time discretizations are based on finite element method and linearized backward difference scheme respectively. \nBoth semi discrete and fully discrete schemes are analyzed with the assumption that the interface is arbitrary but smooth. \nAlmost optimal convergence rate in \\(H^1(\\Omega)\\)-norm is obtained. \nExamples are given to support the theoretical result.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"127 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Approximate solution of nonlinear hyperbolic equations with homogeneous jump conditions\",\"authors\":\"M. O. Adewole\",\"doi\":\"10.33993/jnaat482-1175\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present the error analysis of class of second order nonlinear hyperbolic interface problem where the spatial and time discretizations are based on finite element method and linearized backward difference scheme respectively. \\nBoth semi discrete and fully discrete schemes are analyzed with the assumption that the interface is arbitrary but smooth. \\nAlmost optimal convergence rate in \\\\(H^1(\\\\Omega)\\\\)-norm is obtained. \\nExamples are given to support the theoretical result.\",\"PeriodicalId\":287022,\"journal\":{\"name\":\"Journal of Numerical Analysis and Approximation Theory\",\"volume\":\"127 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Analysis and Approximation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33993/jnaat482-1175\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat482-1175","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximate solution of nonlinear hyperbolic equations with homogeneous jump conditions
We present the error analysis of class of second order nonlinear hyperbolic interface problem where the spatial and time discretizations are based on finite element method and linearized backward difference scheme respectively.
Both semi discrete and fully discrete schemes are analyzed with the assumption that the interface is arbitrary but smooth.
Almost optimal convergence rate in \(H^1(\Omega)\)-norm is obtained.
Examples are given to support the theoretical result.
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