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Numerical Verification Methods for Solutions of Free Boundary Problems

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Mathematical Modeling and Numerical Simulation in Continuum Mechanics

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 19))

Abstract

In this paper, we consider numerical techniques which enable us to verify the existence of solutions for the free boundary problems governed by two kinds of elliptic variational inequalities(EVIs). Based upon the finite element approximations and the explicit a priori error estimates for some simple EVIs, we present effective verification procedures that, through numerical computation, generate a set which includes exact solutions. We describe a survey of the previous works as well as show some newly obtained results up to now.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University 33, Fukuoka, 812-8581, Japan

    Mitsuhiro T. Nakao

  2. Department of Mathematics, Kyungpook National University, Taegu, 702-701, Korea

    Cheon Seoung Ryoo

Authors
  1. Mitsuhiro T. Nakao
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  2. Cheon Seoung Ryoo
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Editor information

Editors and Affiliations

  1. Department of Aerospace Engineering & Engineering Mechanics, The University of Texas at Austin, WRW 215, C0600, Austin, Texas, 78712-1085, USA

    Ivo Babuška

  2. Laboratoire d’Analyse Numérique, Université Pierre et Marie Curie, Boîte courrier 187, 75252, Paris cedex 05, France

    Philippe G. Ciarlet

  3. Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, 753-8512, Yamaguchi, Japan

    Tetsuhiko Miyoshi

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© 2002 Springer-Verlag Berlin Heidelberg

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Nakao, M.T., Ryoo, C.S. (2002). Numerical Verification Methods for Solutions of Free Boundary Problems. In: Babuška, I., Ciarlet, P.G., Miyoshi, T. (eds) Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Lecture Notes in Computational Science and Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56288-4_14

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  • DOI: https://doi.org/10.1007/978-3-642-56288-4_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42399-7

  • Online ISBN: 978-3-642-56288-4

  • eBook Packages: Springer Book Archive

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