Numerical verifications of solutions for elliptic equations with strong nonlinearity

Mitsuhiro Nakao; Nobito Yamamoto

doi:10.1080/01630569108816449

Numerical verifications of solutions for elliptic equations with strong nonlinearity

Mitsuhiro Nakao, Nobito Yamamoto

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

9 Citations (Scopus)

Abstract

Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the infinite dimensional fixed point theorems and the explicit error estimates for finite element approximations. We present detailed verification procedures and numerical examples for the typical model problem: — ∆u=e^u.

Original language	English
Pages (from-to)	535-543
Number of pages	9
Journal	Numerical Functional Analysis and Optimization
Volume	12
Issue number	5-6
DOIs	https://doi.org/10.1080/01630569108816449
Publication status	Published - 1991 Jan 1
Externally published	Yes

ASJC Scopus subject areas

Analysis
Signal Processing
Computer Science Applications
Control and Optimization

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10.1080/01630569108816449

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abstract = "Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the infinite dimensional fixed point theorems and the explicit error estimates for finite element approximations. We present detailed verification procedures and numerical examples for the typical model problem: — ∆u=eu.",

author = "Mitsuhiro Nakao and Nobito Yamamoto",

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AB - Numerical methods for automatic proof of the existence and the local uniqueness of weak solutions of elliptic boundary value problems with strongly nonlinear terms are proposed. They are based on the infinite dimensional fixed point theorems and the explicit error estimates for finite element approximations. We present detailed verification procedures and numerical examples for the typical model problem: — ∆u=eu.

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JO - Numerical Functional Analysis and Optimization

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ER -

Numerical verifications of solutions for elliptic equations with strong nonlinearity

Abstract

ASJC Scopus subject areas

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