{"title":"具有记忆的时变对流-扩散-反应方程的有限体积元逼近","authors":"Anas Rachid, M. Bahaj, R. Fakhar","doi":"10.22034/CMDE.2020.30193.1447","DOIUrl":null,"url":null,"abstract":"Error estimates for element schemes for time-dependent for convection-diffusion-reaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in $L^{2},$ $H^{1}, $ and $W^{1,p }$ norms for $2leq p <infty ,$ are obtained. Inthis paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Finite Volume Element Approximation For Time-dependent Convection-Diffusion-ReactionEquations With Memory\",\"authors\":\"Anas Rachid, M. Bahaj, R. Fakhar\",\"doi\":\"10.22034/CMDE.2020.30193.1447\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Error estimates for element schemes for time-dependent for convection-diffusion-reaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in $L^{2},$ $H^{1}, $ and $W^{1,p }$ norms for $2leq p <infty ,$ are obtained. Inthis paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.\",\"PeriodicalId\":44352,\"journal\":{\"name\":\"Computational Methods for Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-01-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22034/CMDE.2020.30193.1447\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2020.30193.1447","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Finite Volume Element Approximation For Time-dependent Convection-Diffusion-ReactionEquations With Memory
Error estimates for element schemes for time-dependent for convection-diffusion-reaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in $L^{2},$ $H^{1}, $ and $W^{1,p }$ norms for $2leq p