Analysis of a least-squares finite element method for the thin plate problem

被引：3

作者：

Duan, Huo-yuan ^{[1
]}

Gao, Shao-qin ^{[2
]}

Jiang, Bo-nan ^{[3
]}

Tan, Roger C. E. ^{[1
]}

机构：

[1] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore

[2] HeBei Univ, Math & Comp Coll, Baoding City 071002, Hebei Province, Peoples R China

[3] Oakland Univ, Dept Math, Rochester, MI 48309 USA

来源：

APPLIED NUMERICAL MATHEMATICS | 2009年 / 59卷 / 05期

关键词：

Thin plate equation; Deflection-slope-moment-shear force; Least-squares finite element method; STOKES EQUATIONS;

D O I：

10.1016/j.apnum.2008.03.041

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new least-squares finite element method is analyzed for the thin plate problem subject to various boundary conditions (clamped, simply supported and free). The unknown variables are deflection, slope, moment and shear force. The coercivity property is established. As a result, all variables can be approximated by any conforming finite elements. In particular, an H-1-ellipticity is proven for the free thin plate. This indicates that optimal error bounds hold for all variables with the use of equal-order continuous elements. Numerical experiments are performed to confirm the theoretical results obtained. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.

引用

页码：976 / 987

页数：12

共 25 条

[1] ANALYSIS OF LEAST-SQUARES FINITE-ELEMENT METHODS FOR THE STOKES EQUATIONS [J].

BOCHEV, PB ;

GUNZBURGER, MD .

MATHEMATICS OF COMPUTATION, 1994, 63 (208) :479-506

[2] Analysis of least-squares finite element methods for the Navier-Stokes equations [J].

Bochev, PB .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1817-1844

[3] Finite element methods of least-squares type [J].

Bochev, PB ;

Gunzburger, MD .

SIAM REVIEW, 1998, 40 (04) :789-837

[4] Least-squares methods for Stokes equations based on a discrete minus one inner product [J].

Bramble, JH ;

Pasciak, JE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1996, 74 (1-2) :155-173

[5] A negative-norm least squares method for Reissner-Mindlin plates [J].

Bramble, JH ;

Sun, T .

MATHEMATICS OF COMPUTATION, 1998, 67 (223) :901-916

[6] First-order system least squares for the Stokes equations, with application to linear elasticity [J].

Cai, Z ;

Manteuffel, TA ;

McCormick, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (05) :1727-1741

[7] First-order system least squares for second-order partial differential equations .2. [J].

Cai, ZQ ;

Manteuffel, TA ;

McCormick, SF .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1997, 34 (02) :425-454

[8] A FINITE-ELEMENT METHOD FOR 1ST-ORDER ELLIPTIC-SYSTEMS IN 3 DIMENSIONS [J].

CHANG, CL ;

GUNZBURGER, MD .

APPLIED MATHEMATICS AND COMPUTATION, 1987, 23 (02) :171-184

[9] LEAST-SQUARES FINITE-ELEMENT SIMULATION OF TRANSONIC-FLOWS [J].

CHEN, TF ;

FIX, GJ .

APPLIED NUMERICAL MATHEMATICS, 1986, 2 (3-5) :399-408

[10]

Ciarlet P. G., 1988, Three-Dimensional Elasticity I: Nonlinear Theory of Elastic Plates, VI

← 1 2 3 →