Unified analysis of discontinuous Galerkin methods for elliptic problems

被引：2285

作者：

Arnold, DN ^{[1
]}

Brezzi, F

Cockburn, B

Marini, LD

机构：

[1] Univ Minnesota, Inst Math & Its Applicat, Minneapolis, MN 55455 USA

[2] CNR, Ist Anal Numer, I-27100 Pavia, Italy

[3] CNR, Dipartimento Matemat, I-27100 Pavia, Italy

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2002年 / 39卷 / 05期

关键词：

elliptic problems; discontinuous Galerkin; interior penalty;

D O I：

10.1137/S0036142901384162

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We provide a framework for the analysis of a large class of discontinuous methods for second-order elliptic problems. It allows for the understanding and comparison of most of the discontinuous Galerkin methods that have been proposed over the past three decades for the numerical treatment of elliptic problems.

引用

页码：1749 / 1779

页数：31

共 72 条

[1] Discontinuous finite element methods for the simulation of rotating electrical machines
Alotto, P
Bertoni, A
Perugia, I
Schötzau, D
[J]. COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2001, 20 (02) : 448 - 462
[2] [Anonymous], 1976, LECT NOTES PHYS
[3] AN INTERIOR PENALTY FINITE-ELEMENT METHOD WITH DISCONTINUOUS ELEMENTS
ARNOLD, DN
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1982, 19 (04) : 742 - 760
[4] Arnold DN, 2000, LECT NOTES COMP SCI, V11, P89
[5] ARNOLD DN, 1979, THESIS U CHICAGO CHI
[6] APPROXIMATION OF PROBLEMS WITH NON-HOMOGENEOUS LIMITS FOR NON-LINEAR OPERATORS
AUBIN, JP
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1970, 30 (03) : 510 - &
[7] FINITE-ELEMENT METHOD WITH PENALTY
BABUSKA, I
[J]. MATHEMATICS OF COMPUTATION, 1973, 27 (122) : 221 - 228
[8] NONCONFORMING ELEMENTS IN FINITE-ELEMENT METHOD WITH PENALTY
BABUSKA, I
ZLAMAL, M
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1973, 10 (05) : 863 - 875
[9] BAKER GA, 1977, MATH COMPUT, V31, P45, DOI 10.1090/S0025-5718-1977-0431742-5
[10] PIECEWISE SOLENOIDAL VECTOR-FIELDS AND THE STOKES PROBLEM
BAKER, GA
JUREIDINI, WN
KARAKASHIAN, OA
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1990, 27 (06) : 1466 - 1485

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