Numerical verification methods for solutions of the free boundary problem

Kouji Hashimoto, Kenta Kobayashi, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

Abstract

We propose two methods to enclose the solution of an ordinary free boundary problem. The problem is reformulated as a nonlinear boundary value problem on a fixed interval including an unknown parameter. By appropriately setting a functional space that depends on the finite element approximation, the solution is represented as a fixed point of a compact map. Then, by using the finite element projection with constructive error estimates, a Newton-type verification procedure is derived. In addition, numerical examples confirming the effectiveness of current methods are given.

Original languageEnglish
Pages (from-to)523-542
Number of pages20
JournalNumerical Functional Analysis and Optimization
Volume26
Issue number4-5
DOIs
Publication statusPublished - 2005
Externally publishedYes

Keywords

  • Enclosure methods
  • Free boundary
  • Numerical verification methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization

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