Numerical verifications of solutions for nonlinear elliptic equations

Yoshitaka Watanabe; Mitsuhiro T. Nakao

doi:10.1007/BF03167208

Numerical verifications of solutions for nonlinear elliptic equations

Yoshitaka Watanabe^*, Mitsuhiro T. Nakao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.

Original language	English
Pages (from-to)	165-178
Number of pages	14
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	10
Issue number	1
DOIs	https://doi.org/10.1007/BF03167208
Publication status	Published - 1993 Feb
Externally published	Yes

Keywords

finite element method
nonlinear boundary value problems
numerical verification

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/BF03167208

Cite this

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title = "Numerical verifications of solutions for nonlinear elliptic equations",

abstract = "A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.",

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AU - Nakao, Mitsuhiro T.

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AB - A numerical technique which enables us to verify the existence of weak solutions for nonlinear elliptic boundary value problems is proposed. It is based on the infinite dimensional fixed point theorems using the Newton-like operator and the error estimates for finite element approximations. We also present an effective verification procedure which automatically generates the set including the exact solution in a computer. Some numerical examples are illustrated.

KW - finite element method

KW - nonlinear boundary value problems

KW - numerical verification

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ER -

Numerical verifications of solutions for nonlinear elliptic equations

Abstract

Keywords

ASJC Scopus subject areas

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