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Finite Element Method for Hemivariational Inequalities

Theory, Methods and Applications

  • Book
  • © 1999

Overview

Authors:
  1. Jaroslav Haslinger

    1. Charles University, Czech Republic

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  2. Markku Miettinen

    1. University of Jyväskylä, Finland

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  3. Panagiotis D. Panagiotopoulos

    1. Aristotle University, Greece

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Part of the book series: Nonconvex Optimization and Its Applications (NOIA, volume 35)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxv
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  2. Introductory Topics

    1. Front Matter

      Pages 1-1
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    2. Mathematical Preliminaries

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 3-82

    3. Nonsmooth Mechanics. Convex and Nonconvex Problems

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 83-100

  3. Finite Element Approximation of Hemivariational Inequalities

    1. Front Matter

      Pages 101-101
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    2. Approximation of Elliptic Hemivariational Inequalities

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 103-162

    3. Time Dependent Case

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 163-201

  4. Nonsmooth Optimization Methods

    1. Front Matter

      Pages 203-203
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    2. Nonsmooth Optimization Methods

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 205-228

  5. Numerical Examples

    1. Front Matter

      Pages 299-299
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    2. Numerical Examples

      • Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
      Pages 231-258

  6. Back Matter

    Pages 259-260
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Keywords

About this book

Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter.
Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.

Authors and Affiliations

  • Charles University, Czech Republic

    Jaroslav Haslinger

  • University of Jyväskylä, Finland

    Markku Miettinen

  • Aristotle University, Greece

    Panagiotis D. Panagiotopoulos

Bibliographic Information

  • Book Title: Finite Element Method for Hemivariational Inequalities

  • Book Subtitle: Theory, Methods and Applications

  • Authors: Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos

  • Series Title: Nonconvex Optimization and Its Applications

  • DOI: https://doi.org/10.1007/978-1-4757-5233-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1999

  • Hardcover ISBN: 978-0-7923-5951-7Published: 31 August 1999

  • Softcover ISBN: 978-1-4419-4815-1Published: 10 December 2010

  • eBook ISBN: 978-1-4757-5233-5Published: 09 March 2013

  • Series ISSN: 1571-568X

  • Edition Number: 1

  • Number of Pages: XXV, 260

  • Topics: Mathematics, general, Classical Mechanics, Mathematical and Computational Engineering

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