{"title":"Discontinuous Galerkin Method for Nonlinear Quasi-Static Poroelasticity Problems","authors":"Fan Chen,Ming Cui, Chenguang Zhou","doi":"10.4208/ijnam2024-1008","DOIUrl":null,"url":null,"abstract":"This paper is devoted to a discontinuous Galerkin (DG) method for nonlinear quasi-static poroelasticity problems. The fully implicit nonlinear numerical scheme is constructed by\nutilizing DG method for the spatial approximation and the backward Euler method for the temporal discretization. The existence and uniqueness of the numerical solution is proved. Then we\nderive the optimal convergence order estimates in a discrete $H^1$ norm for the displacement and\nin $H^1$ and $L^2$ norms for the pressure. Finally, numerical experiments are supplied to validate the\ntheoretical error estimates of our proposed method.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"13 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Analysis and Modeling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/ijnam2024-1008","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper is devoted to a discontinuous Galerkin (DG) method for nonlinear quasi-static poroelasticity problems. The fully implicit nonlinear numerical scheme is constructed by
utilizing DG method for the spatial approximation and the backward Euler method for the temporal discretization. The existence and uniqueness of the numerical solution is proved. Then we
derive the optimal convergence order estimates in a discrete $H^1$ norm for the displacement and
in $H^1$ and $L^2$ norms for the pressure. Finally, numerical experiments are supplied to validate the
theoretical error estimates of our proposed method.
期刊介绍：
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