Intrinsic finite element methods for the computation of fluxes for Poisson's equation

被引：10

作者：

Ciarlet, P. G. ^{[1
]}

Ciarlet, P., Jr. ^{[2
]}

Sauter, S. A. ^{[3
]}

Simian, C. ^{[4
]}

机构：

[1] City Univ Hong Kong, Dept Math, 83 Tat Chee Ave, Kowloon, Hong Kong, Peoples R China

[2] ENSTA ParisTech, Lab POEMS, CNRS ENSTA INRIA, UMR 7231, 828 Blvd Marechaux, F-91762 Palaiseau, France

[3] Univ Zurich, Inst Math, Winterthurerstr 190, CH-8057 Zurich, Switzerland

[4] Univ Chicago, Dept Comp Sci, 1100 E 58th St, Chicago, IL 60637 USA

来源：

NUMERISCHE MATHEMATIK | 2016年 / 132卷 / 03期

关键词：

Elliptic boundary value problems; Conforming and non-conforming finite element spaces; Intrinsic formulation; ELASTICITY;

D O I：

10.1007/s00211-015-0730-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider an intrinsic approach for the direct computation of the fluxes for problems in potential theory. We develop a general method for the derivation of intrinsic conforming and non-conforming finite element spaces and appropriate lifting operators for the evaluation of the right-hand side from abstract theoretical principles related to the second Strang Lemma. This intrinsic finite element method is analyzed and convergence with optimal order is proved.

引用

页码：433 / 462

页数：30

共 21 条

[1] AMROUCHE C, 1994, CZECH MATH J, V44, P109
[2] [Anonymous], 1998, THEORY APPL SOLID FL
[3] [Anonymous], 1972, HDB MATH FUNCTIONS F
[4] FINITE ELEMENT EXTERIOR CALCULUS FROM HODGE THEORY TO NUMERICAL STABILITY
Arnold, Douglas N.
Falk, Richard S.
Winther, Ragnar
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 47 (02) : 281 - 354
[5] Gauss-Legendre elements: a stable, higher order non-conforming finite element family
Baran, A.
Stoyan, G.
[J]. COMPUTING, 2007, 79 (01) : 1 - 21
[6] Brezzi F., 1991, MIXED HYBRID FINITE, V15
[7] CIARLET P. G., 2002, Classics in Appl. Math., V40
[8] Another approach to linearized elasticity and a new proof of Korn's inequality
Ciarlet, PG
Ciarlet, P
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2005, 15 (02) : 259 - 271
[9] A new approach for approximating linear elasticity problems
Ciarlet, Philippe G.
Ciarlet, Patrick, Jr.
[J]. COMPTES RENDUS MATHEMATIQUE, 2008, 346 (5-6) : 351 - 356
[10] DIRECT COMPUTATION OF STRESSES IN PLANAR LINEARIZED ELASTICITY
Ciarlet, Philippe G.
Ciarlet, Patrick, Jr.
[J]. MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2009, 19 (07) : 1043 - 1064

← 1 2 3 →