THE A POSTERIORI ERROR ESTIMATES OF THE FE APPROXIMATION OF DEFECTIVE EIGENVALUES FOR NON-SELF-ADJOINT EIGENVALUE PROBLEMS

被引：0
作者：
Yang, Yidu [1 ]
Wang, Shixi [1 ]
Bi, Hai [1 ]
机构：
[1] Guizhou Normal Univ, Sch Math Sci, Guiyang 550025, Peoples R China
来源：
SIAM JOURNAL ON NUMERICAL ANALYSIS | 2024年 / 62卷 / 06期
基金：
中国国家自然科学基金;
关键词：
non-self-adjoint eigenvalue problem; defective eigenvalue; finite element method; a posteriori error estimates; clustered eigenvalues; FINITE-ELEMENT METHODS; CONVERGENCE; PRIORI;
D O I：
10.1137/23M162065X
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the a posteriori error estimates of the FEM for defective eigenvalues of non-self-adjoint eigenvalue problems. Using the spectral approximation theory, we establish the abstract a posteriori error formulas for the weighted average of approximate eigenvalues and approximate eigenspace. We then apply the formulas to the defective eigenvalues of elliptic interface problem, derive the a posteriori error estimators, and analyze their reliability and effectiveness. We also provide numerical examples to confirm our theoretical findings.
引用
收藏
页码：2419 / 2438
页数：20
相关论文
共 50 条
  • [1] A posteriori error estimation in finite element analysis
    Ainsworth, M
    Oden, JT
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1997, 142 (1-2) : 1 - 88
  • [2] [Anonymous], 2001, The Finite Element Method and Its Reliability
  • [3] An hp finite element adaptive scheme to solve the Laplace model for fluid-solid vibrations
    Armentano, M. G.
    Padra, C.
    Rodriguez, R.
    Scheble, M.
    [J]. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2011, 200 (1-4) : 178 - 188
  • [4] ERROR ESTIMATES FOR ADAPTIVE FINITE-ELEMENT COMPUTATIONS
    BABUSKA, I
    RHEINBOLDT, WC
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1978, 15 (04) : 736 - 754
  • [5] BABUSv KA I., 1991, Handb. Numer. Anal., VII, P641
  • [6] BANGRTH W., 2003, Adaptive Finite Element Methods for Differential Equation
  • [7] Becker R, 2001, ACT NUMERIC, V10, P1, DOI 10.1017/S0962492901000010
  • [8] Bernardi C, 2000, NUMER MATH, V85, P579, DOI 10.1007/s002110000135
  • [9] ADAPTIVE FINITE ELEMENT METHOD FOR THE MAXWELL EIGENVALUE PROBLEM
    Boffi, Daniele
    Gastaldi, Lucia
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (01) : 478 - 494
  • [10] OPTIMAL CONVERGENCE OF ADAPTIVE FEM FOR EIGENVALUE CLUSTERS IN MIXED FORM
    Boffi, Daniele
    Gallistl, Dietmar
    Gardini, Francesca
    Gastaldi, Lucia
    [J]. MATHEMATICS OF COMPUTATION, 2017, 86 (307) : 2213 - 2237
12345