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

Fingerprint

Numerical Verification
Free Boundary Problem
Nonlinear Boundary Value Problems
Finite Element Approximation
Unknown Parameters
Boundary value problems
Error Estimates
Fixed point
Projection
Finite Element
Numerical Examples
Interval

Keywords

  • Enclosure methods
  • Free boundary
  • Numerical verification methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization

Cite this

Numerical verification methods for solutions of the free boundary problem. / Hashimoto, Kouji; Kobayashi, Kenta; Nakao, Mitsuhiro T.

In: Numerical Functional Analysis and Optimization, Vol. 26, No. 4-5, 2005, p. 523-542.

Research output: Contribution to journalArticle

Hashimoto, Kouji ; Kobayashi, Kenta ; Nakao, Mitsuhiro T. / Numerical verification methods for solutions of the free boundary problem. In: Numerical Functional Analysis and Optimization. 2005 ; Vol. 26, No. 4-5. pp. 523-542.
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