Numerical verifications of solutions for elliptic equations with strong nonlinearity

Mitsuhiro Nakao, Nobito Yamamoto

Research output: Contribution to journalArticle

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=eu.

Original languageEnglish
Pages (from-to)535-543
Number of pages9
JournalNumerical Functional Analysis and Optimization
Volume12
Issue number5-6
DOIs
Publication statusPublished - 1991 Jan 1
Externally publishedYes

Fingerprint

Numerical Verification
Elliptic Boundary Value Problems
Finite Element Approximation
Elliptic Equations
Boundary value problems
Weak Solution
Fixed point theorem
Error Estimates
Numerical methods
Uniqueness
Numerical Methods
Nonlinearity
Numerical Examples
Term
Model

ASJC Scopus subject areas

  • Analysis
  • Signal Processing
  • Computer Science Applications
  • Control and Optimization

Cite this

Numerical verifications of solutions for elliptic equations with strong nonlinearity. / Nakao, Mitsuhiro; Yamamoto, Nobito.

In: Numerical Functional Analysis and Optimization, Vol. 12, No. 5-6, 01.01.1991, p. 535-543.

Research output: Contribution to journalArticle

@article{5053aae5a9534f1ab748885c16ada2b4,
title = "Numerical verifications of solutions for elliptic equations with strong nonlinearity",
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",
year = "1991",
month = "1",
day = "1",
doi = "10.1080/01630569108816449",
language = "English",
volume = "12",
pages = "535--543",
journal = "Numerical Functional Analysis and Optimization",
issn = "0163-0563",
publisher = "Taylor and Francis Ltd.",
number = "5-6",

}

TY - JOUR

T1 - Numerical verifications of solutions for elliptic equations with strong nonlinearity

AU - Nakao, Mitsuhiro

AU - Yamamoto, Nobito

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0001334702&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001334702&partnerID=8YFLogxK

U2 - 10.1080/01630569108816449

DO - 10.1080/01630569108816449

M3 - Article

AN - SCOPUS:0001334702

VL - 12

SP - 535

EP - 543

JO - Numerical Functional Analysis and Optimization

JF - Numerical Functional Analysis and Optimization

SN - 0163-0563

IS - 5-6

ER -