Premium
A correction method for finding lower bounds of eigenvalues of the second‐order elliptic and Stokes operators
Author(s) -
Zhang Yu,
Yang Yidu
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22406
Subject(s) - mathematics , eigenvalues and eigenvectors , eigenfunction , order (exchange) , convergence (economics) , elliptic operator , upper and lower bounds , mathematical analysis , physics , finance , quantum mechanics , economics , economic growth
In this paper, for the second‐order elliptic and Stokes eigenvalue problems with variable coefficients, we propose a correction method to nonconforming eigenvalue approximations and prove that the corrected eigenvalues converge to the exact ones asymptotically from below. In particular, the asymptotic lower bound property of corrected eigenvalues is always valid whether the eigenfunctions are smooth or singular. Finally, we prove that the convergence order of corrected eigenvalues is still the same as that of uncorrected eigenvalues.