Some Remarks on the Rigorous Estimation of Inverse Linear Elliptic Operators

被引：4

作者：

Kinoshita, Takehiko ^{[1
,2
]}

Watanabe, Yoshitaka ^{[3
]}

Nakao, Mitsuhiro T. ^{[4
]}

机构：

[1] Kyoto Univ, Ctr Promot Interdisciplinary Educ & Res, Kyoto 6068501, Japan

[2] Kyoto Univ, Math Sci Res Inst, Kyoto 6068502, Japan

[3] Kyushu Univ, Res Inst Informat Technol, Fukuoka 8128581, Japan

[4] Natl Inst Technol, Sasebo Coll, Nagasaki 8571193, Japan

来源：

SCIENTIFIC COMPUTING, COMPUTER ARITHMETIC, AND VALIDATED NUMERICS (SCAN 2014) | 2016年 / 9553卷

关键词：

BOUNDARY-VALUE-PROBLEMS; FINITE-ELEMENT; EQUATIONS; CONSTANT;

D O I：

10.1007/978-3-319-31769-4_18

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

This paper presents a new numerical method to obtain the rigorous upper bounds of inverse linear elliptic operators. The invertibility of a linearized operator and its norm estimates give important informations when analyzing the nonlinear elliptic partial differential equations (PDEs). The computational costs depend on the concerned elliptic problems as well as the approximation properties of used finite element subspaces, e.g., mesh size or so. We show the proposed new estimate is effective for an intermediate mesh size.

引用

页码：225 / 235

页数：11

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