# Finite Element Method for Hemivariational Inequalities

## Theory, Methods and Applications

• Jaroslav Haslinger
• Markku Miettinen
• Panagiotis D. Panagiotopoulos
Book

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

1. Front Matter
Pages i-xxv
2. ### Introductory Topics

1. Front Matter
Pages 1-1
2. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 3-82
3. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 83-100
3. ### Finite Element Approximation of Hemivariational Inequalities

1. Front Matter
Pages 101-101
2. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 103-162
3. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 163-201
4. ### Nonsmooth Optimization Methods

1. Front Matter
Pages 203-203
2. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 205-228
5. ### Numerical Examples

1. Front Matter
Pages 299-299
2. Jaroslav Haslinger, Markku Miettinen, Panagiotis D. Panagiotopoulos
Pages 231-258
6. Back Matter
Pages 259-260

### Introduction

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.

### Keywords

Finite computational mechanics finite element method function mathematics mechanics optimization

#### Authors and affiliations

• Jaroslav Haslinger
• 1
• Markku Miettinen
• 2
• Panagiotis D. Panagiotopoulos
• 3
1. 1.Charles UniversityCzech Republic
2. 2.University of JyväskyläFinland
3. 3.Aristotle UniversityGreece

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-5233-5
• Copyright Information Springer-Verlag US 1999
• Publisher Name Springer, Boston, MA
• eBook Packages
• Print ISBN 978-1-4419-4815-1
• Online ISBN 978-1-4757-5233-5
• Series Print ISSN 1571-568X
• Buy this book on publisher's site
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