A two-grid discretization scheme for a sort of Steklov eigenvalue problem

被引：0
作者：
Xia, Chao [1 ]
Yang, Yidu [1 ]
Bi, Hai [1 ]
机构：
[1] Guizhou Normal Univ, Sch Math & Comp Sci, Guiyang 550001, Peoples R China
来源：
ADVANCED MATERIALS AND PROCESSES II, PTS 1-3 | 2012年 / 557-559卷
关键词：
Steklov eigenvalue problem; Coupled fluid-solid vibrations; Finite element; Two-grid discretization scheme;
D O I：
10.4028/www.scientific.net/AMR.557-559.2087
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
On the basis of Yang and Bi's work (SIAM J Numer Anal 49, p.1602-1624), this paper discusses a discretization scheme for a sort of Steklov eigenvalue problem and proves the high effiency of the scheme. With the scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid and the solution of a linear algebraic system on the fine grid. And the resulting solution can maintain an asymptotically optimal accuracy. Finally, the numerical results are provided to support the theoretical analysis.
引用
收藏
页码：2087 / 2091
页数：5
相关论文
共 50 条
[31]   A type of multilevel method for the Steklov eigenvalue problem [J].
Xie, Hehu .
IMA JOURNAL OF NUMERICAL ANALYSIS, 2014, 34 (02) :592-608
[32]   A posteriori error estimates for the Steklov eigenvalue problem [J].
Armentano, Maria G. ;
Padra, Claudio .
APPLIED NUMERICAL MATHEMATICS, 2008, 58 (05) :593-601
[33]   An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem [J].
Bi, Hai ;
Li, Hao ;
Yang, Yidu .
APPLIED NUMERICAL MATHEMATICS, 2016, 105 :64-81
[34]   A multilevel Newton's method for the Steklov eigenvalue problem [J].
Yue, Meiling ;
Xu, Fei ;
Xie, Manting .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2022, 48 (03)
[35]   A virtual element method for a biharmonic Steklov eigenvalue problem [J].
Monzon, Gabriel .
ADVANCES IN PURE AND APPLIED MATHEMATICS, 2019, 10 (04) :325-337
[36]   Rearrangements and minimization of the principal eigenvalue of a nonlinear Steklov problem [J].
Emamizadeh, Behrouz ;
Zivari-Rezapour, Mohsen .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2011, 74 (16) :5697-5704
[37]   Nonconforming finite element approximations of the Steklov eigenvalue problem [J].
Yang, Yidu ;
Li, Qin ;
Li, Sirui .
APPLIED NUMERICAL MATHEMATICS, 2009, 59 (10) :2388-2401
[38]   A multilevel Newton’s method for the Steklov eigenvalue problem [J].
Meiling Yue ;
Fei Xu ;
Manting Xie .
Advances in Computational Mathematics, 2022, 48
[39]   A TWO-GRID METHOD FOR THE C0 INTERIOR PENALTY DISCRETIZATION OF THE MONGE-AMPERE EQUATION [J].
Awanou, Gerard ;
Li, Hengguang ;
Malitz, Eric .
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2020, 38 (04) :547-564
[40]   Steklov eigenvalue problem with a-harmonic solutions and variable exponents [J].
Karim, Belhadj ;
Zerouali, Abdellah ;
Chakrone, Omar .
GEORGIAN MATHEMATICAL JOURNAL, 2021, 28 (03) :363-373
12345