{"title":"双孔隙-斯托克斯模型的弱伽勒金有限元法","authors":"Lin Yang,Wei Mu,Hui Peng, Xiuli Wang","doi":"10.4208/ijnam2024-1023","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with\nthe Stokes equations through four interface conditions. In this method, we define several weak\nGalerkin finite element spaces and weak differential operators. We provide the weak Galerkin\nscheme for the model, and establish the well-posedness of the numerical scheme. The optimal\nconvergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of\nthe numerical method with different weak Galerkin elements on different meshes.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model\",\"authors\":\"Lin Yang,Wei Mu,Hui Peng, Xiuli Wang\",\"doi\":\"10.4208/ijnam2024-1023\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with\\nthe Stokes equations through four interface conditions. In this method, we define several weak\\nGalerkin finite element spaces and weak differential operators. We provide the weak Galerkin\\nscheme for the model, and establish the well-posedness of the numerical scheme. The optimal\\nconvergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of\\nthe numerical method with different weak Galerkin elements on different meshes.\",\"PeriodicalId\":50301,\"journal\":{\"name\":\"International Journal of Numerical Analysis and Modeling\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-06-01\",\"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/ijnam2024-1023\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Numerical Analysis and Modeling","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/ijnam2024-1023","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Weak Galerkin Finite Element Method for the Dual-Porosity-Stokes Model
In this paper, we introduce a weak Galerkin finite element method for the dual-porosity-Stokes model. The dual-porosity-Stokes model couples the dual-porosity equations with
the Stokes equations through four interface conditions. In this method, we define several weak
Galerkin finite element spaces and weak differential operators. We provide the weak Galerkin
scheme for the model, and establish the well-posedness of the numerical scheme. The optimal
convergence orders of errors in the energy norm are derived. Finally, we verify the effectiveness of
the numerical method with different weak Galerkin elements on different meshes.
期刊介绍:
The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.