{"title":"H(div;Ω)${\\bf H}(\\mbox{div};\\Omega)$‐椭圆问题","authors":"Raman Kumar, B. Deka","doi":"10.1002/zamm.202200207","DOIUrl":null,"url":null,"abstract":"In this article, we propose the weak Galerkin (WG) finite element schemes for H(div;Ω)${\\bf H}(\\mbox{div}; {\\Omega })$ ‐elliptic problems with and without stabilizers. Optimal orders of convergence are established for the WG approximations in both discrete energy norm and L2 norm. Removing stabilizers from WG finite element methods will simplify the formulations, reduce programming complexity, and may also speed up the computation time. More precisely, for sufficiently smooth solutions, we have proved the supercloseness of order two for the stabilizer free weak Galerkin finite element solution. Several numerical tests are presented to demonstrate the effectiveness of our method.","PeriodicalId":23924,"journal":{"name":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Weak Galerkin finite element methods with and without stabilizers for H(div;Ω)${\\\\bf H}(\\\\mbox{div}; \\\\Omega )$‐elliptic problems\",\"authors\":\"Raman Kumar, B. Deka\",\"doi\":\"10.1002/zamm.202200207\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we propose the weak Galerkin (WG) finite element schemes for H(div;Ω)${\\\\bf H}(\\\\mbox{div}; {\\\\Omega })$ ‐elliptic problems with and without stabilizers. Optimal orders of convergence are established for the WG approximations in both discrete energy norm and L2 norm. Removing stabilizers from WG finite element methods will simplify the formulations, reduce programming complexity, and may also speed up the computation time. More precisely, for sufficiently smooth solutions, we have proved the supercloseness of order two for the stabilizer free weak Galerkin finite element solution. Several numerical tests are presented to demonstrate the effectiveness of our method.\",\"PeriodicalId\":23924,\"journal\":{\"name\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.3000,\"publicationDate\":\"2023-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1002/zamm.202200207\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1002/zamm.202200207","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Weak Galerkin finite element methods with and without stabilizers for H(div;Ω)${\bf H}(\mbox{div}; \Omega )$‐elliptic problems
In this article, we propose the weak Galerkin (WG) finite element schemes for H(div;Ω)${\bf H}(\mbox{div}; {\Omega })$ ‐elliptic problems with and without stabilizers. Optimal orders of convergence are established for the WG approximations in both discrete energy norm and L2 norm. Removing stabilizers from WG finite element methods will simplify the formulations, reduce programming complexity, and may also speed up the computation time. More precisely, for sufficiently smooth solutions, we have proved the supercloseness of order two for the stabilizer free weak Galerkin finite element solution. Several numerical tests are presented to demonstrate the effectiveness of our method.
期刊介绍:
ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.