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A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling

  • Book
  • © 2002

Overview

Authors:
  1. Jörg Steinbach

    1. Augsburg, Germany

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Part of the book series: International Series of Numerical Mathematics (ISNM, volume 136)

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Table of contents (7 chapters)

  1. Front Matter

    Pages ii-x
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  2. Introduction

    • Jörg Steinbach
    Pages 1-6

  3. Derivation of the Evolutionary Variational Inequality Approach

    • Jörg Steinbach
    Pages 7-29

  4. Properties of the Variational Inequality Solution

    • Jörg Steinbach
    Pages 31-72

  5. Finite Volume Approximations for Elliptic Variational Inequalities

    • Jörg Steinbach
    Pages 73-141

  6. Numerical Analysis of the Evolutionary Variational Inequalities

    • Jörg Steinbach
    Pages 143-201

  7. Injection and Compression Moulding as Application Problems

    • Jörg Steinbach
    Pages 203-255

  8. Concluding Remarks

    • Jörg Steinbach
    Pages 257-261

  9. Back Matter

    Pages 263-294
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Keywords

About this book

Since the early 1960s, the mathematical theory of variational inequalities has been under rapid development, based on complex analysis and strongly influenced by 'real-life' application. Many, but of course not all, moving free (Le. , a priori un­ known) boundary problems originating from engineering and economic applica­ tions can directly, or after a transformation, be formulated as variational inequal­ ities. In this work we investigate an evolutionary variational inequality with a memory term which is, as a fixed domain formulation, the result of the application of such a transformation to a degenerate moving free boundary problem. This study includes mathematical modelling, existence, uniqueness and regularity results, numerical analysis of finite element and finite volume approximations, as well as numerical simulation results for applications in polymer processing. Essential parts of these research notes were developed during my work at the Chair of Applied Mathematics (LAM) of the Technical University Munich. I would like to express my sincerest gratitude to K. -H. Hoffmann, the head of this chair and the present scientific director of the Center of Advanced European Studies and Research (caesar), for his encouragement and support. With this work I am fol­ lowing a general concept of Applied Mathematics to which he directed my interest and which, based on application problems, comprises mathematical modelling, mathematical and numerical analysis, computational aspects and visualization of simulation results.

Authors and Affiliations

  • Augsburg, Germany

    Jörg Steinbach

Bibliographic Information

  • Book Title: A Variational Inequality Approach to free Boundary Problems with Applications in Mould Filling

  • Authors: Jörg Steinbach

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-7597-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag 2002

  • Hardcover ISBN: 978-3-7643-6582-0Published: 01 February 2002

  • Softcover ISBN: 978-3-0348-7599-8Published: 18 September 2012

  • eBook ISBN: 978-3-0348-7597-4Published: 06 December 2012

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: X, 294

  • Topics: Partial Differential Equations

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