Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms

被引：4
|
作者：
Liu, Xuefeng [1 ]
机构：
[1] Niigata Univ, Grad Sch Sci & Technol, Niigata, Japan
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 371卷 / 371期
基金：
日本学术振兴会;
关键词：
Explicit eigenvalue bounds; Finite element method; Positive semi-definite bilinear forms; Projection error constants; Verified computation; ERROR CONSTANTS; P-0;
D O I：
10.1016/j.cam.2019.112666
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Recently, the eigenvalue problems formulated with symmetric positive definite bilinear forms have been well investigated with the aim of explicit bounds for the eigenvalues. In this paper, the existing theorems for bounding eigenvalues are further extended to deal with the case of eigenvalue problems defined by positive semi-definite bilinear forms. As an application, the eigenvalue estimation theorems are applied to the error constant estimation for polynomial projections. (C) 2019 Elsevier B.V. All rights reserved.
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