{"title":"A New Weak Galerkin Method with Weakly Enforced Dirichlet Boundary Condition","authors":"Dan Li, Yiqiang Li null, Zhanbin Yuan","doi":"10.4208/ijnam2023-1028","DOIUrl":null,"url":null,"abstract":". A new weak Galerkin method with weakly enforced Dirichlet boundary condition is proposed and analyzed for the second order elliptic problems. Two penalty terms are incorporated into the weak Galerkin method to enforce the boundary condition in the weak sense. The new numerical scheme is designed by using the locally constructed weak gradient. Optimal order error estimates are established for the numerical approximation in the energy norm and usual L 2 norm. Moreover, by using the Schur complement technique, the unknowns of the numerical scheme are only de(cid:12)ned on the boundary of each piecewise element and an e(cid:11)ective implementation of the reduced global system is presented. Some numerical experiments are reported to demonstrate the accuracy and e(cid:14)ciency of the proposed method.","PeriodicalId":50301,"journal":{"name":"International Journal of Numerical Analysis and Modeling","volume":"10 1","pages":"0"},"PeriodicalIF":1.3000,"publicationDate":"2023-06-01","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":"1085","ListUrlMain":"https://doi.org/10.4208/ijnam2023-1028","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
. A new weak Galerkin method with weakly enforced Dirichlet boundary condition is proposed and analyzed for the second order elliptic problems. Two penalty terms are incorporated into the weak Galerkin method to enforce the boundary condition in the weak sense. The new numerical scheme is designed by using the locally constructed weak gradient. Optimal order error estimates are established for the numerical approximation in the energy norm and usual L 2 norm. Moreover, by using the Schur complement technique, the unknowns of the numerical scheme are only de(cid:12)ned on the boundary of each piecewise element and an e(cid:11)ective implementation of the reduced global system is presented. Some numerical experiments are reported to demonstrate the accuracy and e(cid:14)ciency of the proposed method.
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.
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