Numerical verification of solutions for variational inequalities

Cheon Seoung Ryoo, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

In this paper, we consider a numerical technique that enables us to verify the existence of solutions for variational inequalities. This technique is based on the infinite dimensional fixed point theorems and explicit error estimates for finite element approximations. Using the finite element approximations and explicit a priori error estimates for obstacle problems, we present an effective verification procedure that through numerical computation generates a set which includes the exact solution. Further, a numerical example for an obstacle problem is presented.

Original languageEnglish
Pages (from-to)305-320
Number of pages16
JournalNumerische Mathematik
Volume81
Issue number2
Publication statusPublished - 1998 Dec
Externally publishedYes

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Numerical Verification
Obstacle Problem
Finite Element Approximation
Variational Inequalities
A Priori Error Estimates
Numerical Techniques
Numerical Computation
Fixed point theorem
Error Estimates
Existence of Solutions
Exact Solution
Verify
Numerical Examples

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

Numerical verification of solutions for variational inequalities. / Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.

In: Numerische Mathematik, Vol. 81, No. 2, 12.1998, p. 305-320.

Research output: Contribution to journalArticle

Ryoo, CS & Nakao, MT 1998, 'Numerical verification of solutions for variational inequalities', Numerische Mathematik, vol. 81, no. 2, pp. 305-320.
Ryoo, Cheon Seoung ; Nakao, Mitsuhiro T. / Numerical verification of solutions for variational inequalities. In: Numerische Mathematik. 1998 ; Vol. 81, No. 2. pp. 305-320.
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