{"title":"多面体区域椭圆型问题hp -DGFEM的指数收敛性","authors":"D. Schötzau, C. Schwab, T. Wihler, M. Wirz","doi":"10.3929/ETHZ-A-010406377","DOIUrl":null,"url":null,"abstract":"We review the recent results of D. Schotzau et al. (hp-dGFEM for elliptic problems in polyhedra. I: Stability and quasioptimality on geometric meshes. Technical report 2009-28, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013; hp-dGFEM for elliptic problems in polyhedra. II: Exponential convergence. Technical report 2009-29, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013), and establish the exponential convergence of hp-version discontinuous Galerkin finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and constant coefficients in three-dimsional and axiparallel polyhedra. The exponential rates are confirmed in a series of numerical tests.","PeriodicalId":22276,"journal":{"name":"The annual research report","volume":"14 1","pages":"57-73"},"PeriodicalIF":0.0000,"publicationDate":"2014-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Exponential Convergence of hp -DGFEM for Elliptic Problems in Polyhedral Domains\",\"authors\":\"D. Schötzau, C. Schwab, T. Wihler, M. Wirz\",\"doi\":\"10.3929/ETHZ-A-010406377\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We review the recent results of D. Schotzau et al. (hp-dGFEM for elliptic problems in polyhedra. I: Stability and quasioptimality on geometric meshes. Technical report 2009-28, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013; hp-dGFEM for elliptic problems in polyhedra. II: Exponential convergence. Technical report 2009-29, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013), and establish the exponential convergence of hp-version discontinuous Galerkin finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and constant coefficients in three-dimsional and axiparallel polyhedra. The exponential rates are confirmed in a series of numerical tests.\",\"PeriodicalId\":22276,\"journal\":{\"name\":\"The annual research report\",\"volume\":\"14 1\",\"pages\":\"57-73\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The annual research report\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3929/ETHZ-A-010406377\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The annual research report","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3929/ETHZ-A-010406377","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Exponential Convergence of hp -DGFEM for Elliptic Problems in Polyhedral Domains
We review the recent results of D. Schotzau et al. (hp-dGFEM for elliptic problems in polyhedra. I: Stability and quasioptimality on geometric meshes. Technical report 2009-28, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013; hp-dGFEM for elliptic problems in polyhedra. II: Exponential convergence. Technical report 2009-29, Seminar for applied mathematics, ETH Zurich, 2009. To appear in SIAM J Numer Anal, 2013), and establish the exponential convergence of hp-version discontinuous Galerkin finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and constant coefficients in three-dimsional and axiparallel polyhedra. The exponential rates are confirmed in a series of numerical tests.
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