A New Adaptive Mixed Finite Element Method Based on Residual Type A Posterior Error Estimates for the Stokes Eigenvalue Problem

被引：16

作者：

Han, Jiayu ^{[1
]}

Zhang, Zhimin ^{[2
]}

Yang, Yidu ^{[1
]}

机构：

[1] Guizhou Normal Univ, Sch Math & Comp Sci, Guiyang 550001, Peoples R China

[2] Beijing Computat Sci Res Ctr, Lab Appl Math, Beijing 100084, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2015年 / 31卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Stokes eigenvalue problem; mixed finite element; Rayleigh quotient iteration; a posterior error estimates; adaptive algorithm; DISCRETIZATIONS;

D O I：

10.1002/num.21891

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we combine mixed finite element method, multiscale discretization, and Rayleigh quotient iteration to propose a new adaptive algorithm based on residual type a posterior error estimates for the Stokes eigenvalue problem. Both reliability and efficiency of the error indicator are proved. The efficiency of the algorithm is also investigated using Chen's Innovation Finite Element Method (iFEM) package. Numerical results are satisfying.(c) 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 31-53, 2015

引用

页码：31 / 53

页数：23

共 50 条

[31] Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem
Yang YiDu
Jiang Wei
SCIENCE CHINA-MATHEMATICS, 2013, 56 (06) : 1313 - 1330
[32] Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem
YiDu Yang
Wei Jiang
Science China Mathematics, 2013, 56 : 1313 - 1330
[33] Upper spectral bounds and a posteriori error analysis of several mixed finite element approximations for the Stokes eigenvalue problem
YANG YiDu
JIANG Wei
Science China Mathematics, 2013, 56 (06) : 1308 - 1325
[34] Residual-based a posteriori error estimates for a nonconforming finite element discretization of the Stokes–Darcy coupled problem: isotropic discretization
Nicaise S.
Ahounou B.
Houedanou W.
Afrika Matematika, 2016, 27 (3-4) : 701 - 729
[35] An Efficient Algorithm with Stabilized Finite Element Method for the Stokes Eigenvalue Problem
Weng, Zhifeng
Cai, Yaoxiong
MATHEMATICAL PROBLEMS IN ENGINEERING, 2017, 2017
[36] A posteriori error estimates for a Virtual Element Method for the Steklov eigenvalue problem
Mora, David
Rivera, Gonzalo
Rodriguez, Rodolfo
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 74 (09) : 2172 - 2190
[37] A priori error estimates for a coupled finite element method and mixed finite element method for a fluid-solid interaction problem
Feng, XB
Xie, ZH
IMA JOURNAL OF NUMERICAL ANALYSIS, 2004, 24 (04) : 671 - 698
[38] AN ADAPTIVE FINITE ELEMENT METHOD FOR THE ELASTIC TRANSMISSION EIGENVALUE PROBLEM
ZHANG, X. U. Q. I. N. G.
HAN, J. I. A. Y. U.
YANG, Y. I. D. U.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2022,
[39] ERROR-ESTIMATES FOR A MIXED FINITE-ELEMENT APPROXIMATION OF THE STOKES EQUATIONS
VERFURTH, R
RAIRO-ANALYSE NUMERIQUE-NUMERICAL ANALYSIS, 1984, 18 (02): : 175 - 182
[40] AN ADAPTIVE FINITE ELEMENT METHOD FOR THE ELASTIC TRANSMISSION EIGENVALUE PROBLEM
Zhang, Xuqing
Han, Jiayu
Yang, Yidu
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2023, 28 (02): : 1367 - 1392

← 1 2 3 4 5 →