New High Accuracy Analysis of a Double Set Parameter Nonconforming Element for the Clamped Kirchhoff Plate Unilaterally Constrained by an Elastic Obstacle

被引：0

作者：

Shi, Dongyang ^{[1
]}

Pei, Lifang ^{[1
]}

机构：

[1] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China

来源：

MATHEMATICS | 2020年 / 8卷 / 11期

基金：

中国国家自然科学基金;

关键词：

elastic obstacle; Kirchhoff plate; non-C-0; FEM; double set parameter method; high accuracy error estimate; FINITE-ELEMENT; SUPERCONVERGENCE; CONVERGENCE;

D O I：

10.3390/math8112038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a non-C-0 double set parameter finite element method is presented for the clamped Kirchhoff plate with an elastic unilateral obstacle. A new high accuracy error estimate with order O(h(2)) in the broken energy norm is derived by use of a series of novel approaches, including some special features of the element and an incomplete biquadratic interpolation operator. At the same time, some experimental results are provided to verify the theoretical analysis.

引用

页码：1 / 13

页数：13

共 32 条

[1]

Brenner S.C., 1998, The Mathematical Theory of Finite Element Methods

[2] A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates [J].

Brenner, Susanne C. ;

Sung, Li-yeng ;

Zhang, Hongchao ;

Zhang, Yi .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2013, 254 :31-42

[3] FINITE ELEMENT METHODS FOR THE DISPLACEMENT OBSTACLE PROBLEM OF CLAMPED PLATES [J].

Brenner, Susanne C. ;

Sung, Li-Yeng ;

Zhang, Yi .

MATHEMATICS OF COMPUTATION, 2012, 81 (279) :1247-1262

[4]

Chen SC, 2005, J COMPUT MATH, V23, P185

[5]

CHEN SC, 2005, J ENG MATH, V22, P599

[6]

CHEN SC, 1991, NUMER MATH SINICA, V3, P286

[7] An anisotropic, superconvergent nonconforming plate finite element [J].

Chen, Shaochun ;

Yin, Li ;

Mao, Shipeng .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2008, 220 (1-2) :96-110

[8]

Chen SC, 2010, INT J NUMER ANAL MOD, V7, P766

[9]

CIARLET P.G., 2002, The Finite Element Method for Elliptic Problems

[10] REGULARITY OF SOLUTION OF BIHARMONIC VARIATIONAL INEQUALITY [J].

FREHSE, J .

MANUSCRIPTA MATHEMATICA, 1973, 9 (01) :91-103

← 1 2 3 4 →