A numerical approach to the proof of existence of solutions for elliptic problems

Mitsuhiro T. Nakao*

*この研究の対応する著者

研究成果: Article査読

66 被引用数 (Scopus)

抄録

In this paper, we describe a method which proves by computers the existence of weak solutions for linear elliptic boundary value problems of second order. It is shown that we can constitute the computing procedures to verify the existence, uniqueness and inclusion set of a solution based on Schauder's fixed point theorem. Using the finite element approximations for some simple Poisson's equations and the results of error estimates, we generate iteratively a set sequence composed of functions and attempt to construct automatically the set including the exact solution. Further, the conditions of verifiability by this method are considered and some numerical examples of verification are presented.

本文言語English
ページ(範囲)313-332
ページ数20
ジャーナルJapan Journal of Applied Mathematics
5
2
DOI
出版ステータスPublished - 1988 6月
外部発表はい

ASJC Scopus subject areas

  • 工学(全般)
  • 応用数学

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