{"title":"A Coupled Method Combining Crouzeix-Raviart Nonconforming and Node Conforming Finite Element Spaces for Boit Consolidation Model","authors":"Yuping Zeng, M. Zhong","doi":"10.4208/jcm.2212-m2021-0231","DOIUrl":null,"url":null,"abstract":"A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results. Mathematics","PeriodicalId":50225,"journal":{"name":"Journal of Computational Mathematics","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jcm.2212-m2021-0231","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
A mixed finite element method is presented for the Biot consolidation problem in poroe-lasticity. More precisely, the displacement is approximated by using the Crouzeix-Raviart nonconforming finite elements, while the fluid pressure is approximated by using the node conforming finite elements. The well-posedness of the fully discrete scheme is established, and a corresponding priori error estimate with optimal order in the energy norm is also derived. Numerical experiments are provided to validate the theoretical results. Mathematics
期刊介绍：
Journal of Computational Mathematics (JCM) is an international scientific computing journal founded by Professor Feng Kang in 1983, which is the first Chinese computational mathematics journal published in English. JCM covers all branches of modern computational mathematics such as numerical linear algebra, numerical optimization, computational geometry, numerical PDEs, and inverse problems. JCM has been sponsored by the Institute of Computational Mathematics of the Chinese Academy of Sciences.
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