{"title":"Convergence of adaptive stochastic collocation with finite elements","authors":"M. Feischl, Andrea Scaglioni","doi":"10.5445/IR/1000125783","DOIUrl":null,"url":null,"abstract":"We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.","PeriodicalId":10572,"journal":{"name":"Comput. Math. Appl.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Comput. Math. Appl.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5445/IR/1000125783","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 8
Abstract
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove for the first time convergence of a stochastic collocation algorithm which adaptively enriches the parameter space as well as refines the finite element meshes.
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