{"title":"二阶椭圆方程的杂化不连续伽辽金法的超收敛性","authors":"Minam Moon, Yang Hwan Lim","doi":"10.12941/JKSIAM.2016.20.295","DOIUrl":null,"url":null,"abstract":"A BSTRACT . We propose a projection-based analysis of a new hybridizable discontinuous Galerkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses L 2 − projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p +1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"22 1","pages":"295-308"},"PeriodicalIF":0.3000,"publicationDate":"2016-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"SUPERCONVERGENCE OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS\",\"authors\":\"Minam Moon, Yang Hwan Lim\",\"doi\":\"10.12941/JKSIAM.2016.20.295\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A BSTRACT . We propose a projection-based analysis of a new hybridizable discontinuous Galerkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses L 2 − projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p +1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.\",\"PeriodicalId\":41717,\"journal\":{\"name\":\"Journal of the Korean Society for Industrial and Applied Mathematics\",\"volume\":\"22 1\",\"pages\":\"295-308\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2016-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Korean Society for Industrial and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12941/JKSIAM.2016.20.295\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Korean Society for Industrial and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12941/JKSIAM.2016.20.295","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
SUPERCONVERGENCE OF HYBRIDIZABLE DISCONTINUOUS GALERKIN METHOD FOR SECOND-ORDER ELLIPTIC EQUATIONS
A BSTRACT . We propose a projection-based analysis of a new hybridizable discontinuous Galerkin method for second order elliptic equations. The method is more advantageous than the standard HDG method in a sense that the new method has higher-order accuracy and lower computational cost, and is more flexible. Notable distinctions of our new method, when compared to the standard HDG emthod, are that our method uses L 2 − projection and suitable stabilization parameter depending on a mesh size for superconvergence. We show that the error for the solution of the equation converges with order p + 2 when we only use polynomials of degree p +1 as a finite element space without postprocessing. After establishing the theory, we carry out numerical tests to demonstrate and ensure that the proposed method is effective and accurate in practice.