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.

引用

页码：36 / 46

页数：11

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