Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems

被引：8

作者：

Carstensen, C. ^{[1
]}

Hoppe, R. H. W. ^{[2
,3
]}

机构：

[1] Humboldt Univ, Dept Math, D-10099 Berlin, Germany

[2] Univ Houston, Dept Math, Houston, TX 77204 USA

[3] Univ Augsburg, Inst Math, D-86159 Augsburg, Germany

来源：

JOURNAL OF NUMERICAL MATHEMATICS | 2009年 / 17卷 / 01期

基金：

美国国家科学基金会;

关键词：

a posteriori error analysis; unified framework; non-standard finite element methods; H(curl)-elliptic problems; EDDY-CURRENT CALCULATIONS; UNIFYING THEORY; TRACES; EQUATIONS;

D O I：

10.1515/JNUM.2009.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A unified framework for a residual- based a posteriori error analysis of standard conforming finite element methods as well as non-standard techniques such as nonconforming and mixed methods has been developed in [20-24]. This paper provides such a framework for an a posteriori error control of nonconforming finite element discretizations of H(curl)-elliptic problems as they arise from low-frequency electromagnetics. These nonconforming approximations include the interior penalty discontinuous Galerkin ( IPDG) approach considered in [33,34], and mortar edge element approximations studied in [10,28-31,41,48].

引用

页码：27 / 44

页数：18

共 50 条

[1] Unified Framework for an A Posteriori Error Analysis of Non-Standard Finite Element Approximations of H(curl)-Elliptic Problems
Carstensen, C.
Hoppe, Ronald H. W.
[J]. ICEAA: 2009 INTERNATIONAL CONFERENCE ON ELECTROMAGNETICS IN ADVANCED APPLICATIONS, VOLS 1 AND 2, 2009, : 754 - +
[2] A posteriori error control for finite element approximations of elliptic eigenvalue problems
Vincent Heuveline
Rolf Rannacher
[J]. Advances in Computational Mathematics, 2001, 15 : 107 - 138
[3] A posteriori error estimates for mixed finite element approximations of elliptic problems
Mats G. Larson
Axel Målqvist
[J]. Numerische Mathematik, 2008, 108 : 487 - 500
[4] A posteriori error control for finite element approximations of elliptic eigenvalue problems
Heuveline, V
Rannacher, R
[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2001, 15 (1-4) : 107 - 138
[5] A posteriori error estimates for mixed finite element approximations of elliptic problems
Larson, Mats G.
Malqvist, Axel
[J]. NUMERISCHE MATHEMATIK, 2008, 108 (03) : 487 - 500
[6] A posteriori and a priori error analysis or finite element approximations of self-adjoint elliptic eigenvalue problems
Larson, MG
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2000, 38 (02) : 608 - 625
[7] A posteriori error analysis for stabilised finite element approximations of transport problems
Houston, P
Rannacher, R
Süli, E
[J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2000, 190 (11-12) : 1483 - 1508
[8] A posteriori error analysis and adaptivity for finite element approximations of hyperbolic problems
Süli, E
[J]. AN INTRODUCTION TO RECENT DEVELOPMENTS IN THEORY AND NUMERICS FOR CONSERVATION LAWS, 1999, 5 : 123 - 194
[9] A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes
Ern, Alexandre
Vohralik, Martin
[J]. FINITE VOLUMES FOR COMPLEX APPLICATIONS VI: PROBLEMS & PERSPECTIVES, VOLS 1 AND 2, 2011, 4 : 821 - +
[10] A posteriori error estimator for mixed interior penalty discontinuous Galerkin finite element method for the H(curl)-elliptic problems
Tang, Ming
Xing, Xiaoqing
Zhong, Liuqiang
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 436

← 1 2 3 4 5 →