Stabilization of low-order mixed finite elements for the plane elasticity equations

被引：4
|
作者：
Li, Zhenzhen [1 ]
Chen, Shaochun [2 ]
Qu, Shuanghong [1 ]
Li, Minghao [3 ]
机构：
[1] Zhengzhou Univ Light Ind, Coll Math & Informat Sci, Zhengzhou 450002, Peoples R China
[2] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Peoples R China
[3] Henan Univ Technol, Coll Sci, Zhengzhou 450001, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 73卷 / 03期
关键词：
Plane elasticity equations; Low order elements; Weak inf-sup condition; Stabilization; LEAST-SQUARES METHODS; LINEAR ELASTICITY; STOKES EQUATIONS; SYMMETRIC FORMULATION; RECTANGULAR GRIDS; FAMILY; APPROXIMATIONS; TENSORS;
D O I：
10.1016/j.camwa.2016.11.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the mixed finite element method of the plane elasticity equations based on the Hellinger-Reissner variational principle. Low order mixed finite element spaces are used to approximate the stress and the displacement. Based on the local polynomial projection stabilization method, we present a stabilization scheme for the pairs to overcome the lack of the inf-supcondition. The stability is proved and the error estimate is derived. At last, two numerical examples are implemented to test the stability and effectiveness of the proposed method. These pairs are very convenient in the numerical implementation for the mixed form of the plane elasticity equations. (C) 2016 Elsevier Ltd. All rights reserved.
引用
收藏
页码：363 / 373
页数：11
相关论文
共 50 条
  • [41] A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
    Jun Hu
    ShangYou Zhang
    Science China Mathematics, 2015, 58 : 297 - 307
  • [42] A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
    Hu Jun
    Zhang ShangYou
    SCIENCE CHINA-MATHEMATICS, 2015, 58 (02) : 297 - 307
  • [43] Stress mixed polyhedral finite elements for two-scale elasticity models with relaxed symmetry
    Devloo, Philippe R. B.
    Fernandes, Jeferson W. D.
    Gomes, Sonia M.
    Shauer, Nathan
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2024, 159 : 302 - 318
  • [44] LQG-Balanced Truncation Low-Order Controller for Stabilization of Laminar Flows
    Benner, Peter
    Heiland, Jan
    ACTIVE FLOW AND COMBUSTION CONTROL 2014, 2015, 127 : 365 - 379
  • [45] Some low order nonconforming mixed finite elements combined with Raviart–Thomas elements for a coupled Stokes–Darcy model
    Peiqi Huang
    Jinru Chen
    Japan Journal of Industrial and Applied Mathematics, 2013, 30 : 565 - 584
  • [46] STABILIZATION OF HIGH ASPECT RATIO MIXED FINITE ELEMENTS FOR INCOMPRESSIBLE FLOW
    Ainsworth, Mark
    Barrenechea, Gabriel R.
    Wachtel, Andreas
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2015, 53 (02) : 1107 - 1120
  • [47] SUPERCLOSENESS AND SUPERCONVERGENCE OF STABILIZED LOW-ORDER FINITE ELEMENT DISCRETIZATIONS OF THE STOKES PROBLEM
    Eichel, Hagen
    Tobiska, Lutz
    Xie, Hehu
    MATHEMATICS OF COMPUTATION, 2011, 80 (274) : 697 - 722
  • [48] STABILIZATION OF HIGHER ORDER SCHRODINGER EQUATIONS ON A FINITE INTERVAL: PART I
    Batal, Ahmet
    Ozsari, Turker
    Yilmaz, Kemal Cem
    EVOLUTION EQUATIONS AND CONTROL THEORY, 2021, 10 (04): : 861 - 919
  • [49] Partial Relaxation of C0 Vertex Continuity of Stresses of Conforming Mixed Finite Elements for the Elasticity Problem
    Hu, Jun
    Ma, Rui
    COMPUTATIONAL METHODS IN APPLIED MATHEMATICS, 2021, 21 (01) : 89 - 108
  • [50] SUPERCONVERGENCE ANALYSIS OF THE STABLE CONFORMING RECTANGULAR MIXED FINITE ELEMENTS FOR THE LINEAR ELASTICITY PROBLEM
    Shi, Dongyang
    Li, Minghao
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 2014, 32 (02) : 205 - 214
12345