Some improvements of invertibility verifications for second-order linear elliptic operators

被引：4
|
作者：
Watanabe, Yoshitaka [1 ]
Kinoshita, Takehiko [1 ]
Nakao, Mitsuhiro T. [2 ]
机构：
[1] Kyushu Univ, Res Inst Informat Technol, Nishi Ku, 744 Motooka, Fukuoka 8190395, Japan
[2] Waseda Univ, Fac Sci & Engn, Shinjuku Ku, 3-4-1 Okubo, Tokyo 1698555, Japan
来源：
APPLIED NUMERICAL MATHEMATICS | 2020年 / 154卷 / 154期
基金：
日本科学技术振兴机构;
关键词：
Numerical verification; Solvability of linear problem; Differential operators; NUMERICAL VERIFICATION; ERROR ESTIMATION; EQUATIONS; INVERSE; BOUNDS; EXISTENCE; CONSTANT; NORM;
D O I：
10.1016/j.apnum.2020.03.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper presents some computer-assisted procedures to prove the invertibility of a second-order linear elliptic operator and to compute a bound for the norm of its inverse. These approaches are based on constructive L-2-norm estimates of the Laplacian and improve on previous procedures that use projection and a priori error estimations. Several examples which confirm the actual effectiveness of the procedures are reported. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
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页码：36 / 46
页数：11
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