Extrapolation and superconvergence of the Steklov eigenvalue problem

被引：0
|
作者：
Mingxia Li
Qun Lin
Shuhua Zhang
机构：
[1] Chinese Academy of Sciences,Academy of Mathematics and Systems Science
[2] Tianjin University of Finance and Economics,Research Center for Mathematics and Economics
来源：
Advances in Computational Mathematics | 2010年 / 33卷
关键词：
The Steklov eigenvalue problem; Graded meshes; Richardson extrapolation; Superconvergence; A posteriori error estimators; 76S05; 45K05; 65M12; 65M60; 65R20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
On the basis of a transform lemma, an asymptotic expansion of the bilinear finite element is derived over graded meshes for the Steklov eigenvalue problem, such that the Richardson extrapolation can be applied to increase the accuracy of the approximation, from which the approximation of O(h3.5) is obtained. In addition, by means of the Rayleigh quotient acceleration technique and an interpolation postprocessing method, the superconvergence of the bilinear finite element is presented over graded meshes for the Steklov eigenvalue problem, and the approximation of O(h3) is gained. Finally, numerical experiments are provided to demonstrate the theoretical results.
引用
收藏
页码：25 / 44
页数：19
相关论文
共 50 条
  • [41] Boundary element approximation of Steklov eigenvalue problem for Helmholtz equation
    Tang, WJ
    Guan, Z
    Han, HD
    JOURNAL OF COMPUTATIONAL MATHEMATICS, 1998, 16 (02) : 165 - 178
  • [42] MULTISCALE COMPUTATION OF A STEKLOV EIGENVALUE PROBLEM WITH RAPIDLY OSCILLATING COEFFICIENTS
    Cao, Li-Qun
    Zhang, Lei
    Allegretto, Walter
    Lin, Yanping
    INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (01) : 42 - 73
  • [43] THE ASYMPTOTIC BEHAVIOUR OF THE p(x)-LAPLACIAN STEKLOV EIGENVALUE PROBLEM
    Yu, Lujuan
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2020, 25 (07): : 2621 - 2637
  • [44] Resonant Steklov eigenvalue problem involving the (p, q)-Laplacian
    A. Zerouali
    B. Karim
    O. Chakrone
    A. Boukhsas
    Afrika Matematika, 2019, 30 : 171 - 179
  • [45] A shape optimization problem for the first mixed Steklov–Dirichlet eigenvalue
    Dong-Hwi Seo
    Annals of Global Analysis and Geometry, 2021, 59 : 345 - 365
  • [46] Resonant Steklov eigenvalue problem involving the (p, q)-Laplacian
    Zerouali, A.
    Karim, B.
    Chakrone, O.
    Boukhsas, A.
    AFRIKA MATEMATIKA, 2019, 30 (1-2) : 171 - 179
  • [47] A three dimensional Steklov eigenvalue problem with exponential nonlinearity on the boundary
    Pagani, Carlo Domenico
    Pierotti, Dario
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2013, 79 : 28 - 40
  • [48] Numerical studies of the Steklov eigenvalue problem via conformal mappings
    Alhejaili, Weaam
    Kaoc, Chiu-Yen
    APPLIED MATHEMATICS AND COMPUTATION, 2019, 347 : 785 - 802
  • [49] OPTIMALITY CONDITIONS OF THE FIRST EIGENVALUE OF A FOURTH ORDER STEKLOV PROBLEM
    Laskawy, Monika
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2017, 16 (05) : 1843 - 1859
  • [50] A STABILITY RESULT FOR THE STEKLOV LAPLACIAN EIGENVALUE PROBLEM WITH A SPHERICAL OBSTACLE
    Paoli, Gloria
    Piscitelli, Gianpaolo
    Sannipoli, Rossanno
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2021, 20 (01) : 145 - 158
12345