Gradient Recovery for the Crouzeix-Raviart Element

被引：16
|
作者：
Guo, Hailong [1 ]
Zhang, Zhimin [1 ,2 ]
机构：
[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA
[2] Beijing Computat Sci Res Ctr, Beijing 100084, Peoples R China
来源：
JOURNAL OF SCIENTIFIC COMPUTING | 2015年 / 64卷 / 02期
基金：
美国国家科学基金会; 中国国家自然科学基金;
关键词：
Nonconforming; The Crouzeix-Raviart element; Gradient recovery; Superconvergence; Polynomial preserving; POSTERIORI ERROR ESTIMATORS; PART I; SUPERCONVERGENCE; GRIDS;
D O I：
10.1007/s10915-014-9939-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A gradient recovery method for the Crouzeix-Raviart element is proposed and analyzed. The proposed method is based on local discrete least square fittings. It is proven to preserve quadratic polynomials and be a bounded linear operator. Numerical examples indicate that it can produce a superconvergent gradient approximation for both elliptic equations and Stokes equations. In addition, it provides an asymptotically exact posteriori error estimators for the Crouzeix-Raviart element.
引用
收藏
页码：456 / 476
页数：21
相关论文
共 50 条
  • [1] Gradient Recovery for the Crouzeix–Raviart Element
    Hailong Guo
    Zhimin Zhang
    [J]. Journal of Scientific Computing, 2015, 64 : 456 - 476
  • [2] Superconvergent Cluster Recovery Method for the Crouzeix-Raviart Element
    Zhang, Yidan
    Chen, Yaoyao
    Huang, Yunqing
    Yi, Nianyu
    [J]. NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, 2021, 14 (02) : 508 - 526
  • [3] ASYMPTOTICALLY EXACT A POSTERIORI ERROR ESTIMATES OF EIGENVALUES BY THE CROUZEIX-RAVIART ELEMENT AND ENRICHED CROUZEIX-RAVIART ELEMENT
    Hu, Jun
    Ma, Limin
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2020, 42 (02): : A797 - A821
  • [4] Forty Years of the Crouzeix-Raviart Element
    Brenner, Susanne C.
    [J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2015, 31 (02) : 367 - 396
  • [5] ADAPTIVE CROUZEIX-RAVIART BOUNDARY ELEMENT METHOD
    Heuer, Norbert
    Karkulik, Michael
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2015, 49 (04): : 1193 - 1217
  • [6] Superconvergence of the Crouzeix-Raviart element for elliptic equation
    Zhang, Yidan
    Huang, Yunqing
    Yi, Nianyu
    [J]. ADVANCES IN COMPUTATIONAL MATHEMATICS, 2019, 45 (5-6) : 2833 - 2844
  • [7] Superconvergence of the Crouzeix-Raviart element for elliptic equation
    Yidan Zhang
    Yunqing Huang
    Nianyu Yi
    [J]. Advances in Computational Mathematics, 2019, 45 : 2833 - 2844
  • [8] ASYMPTOTIC EXPANSIONS OF EIGENVALUES BY BOTH THE CROUZEIX-RAVIART AND ENRICHED CROUZEIX-RAVIART ELEMENTS
    Hu, Jun
    Ma, Limin
    [J]. MATHEMATICS OF COMPUTATION, 2022, 91 (333) : 75 - 109
  • [9] Discontinuous Galerkin and the Crouzeix-Raviart element: Application to elasticity
    Hansbo, P
    Larson, MG
    [J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2003, 37 (01): : 63 - 72
  • [10] A general quadratic enrichment of the Crouzeix-Raviart finite element
    Nudo, Federico
    [J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2024, 451
12345