Finite Element Method for Hemivariational Inequalities

Theory, Methods and Applications
1999
ISBN: 978-0-7923-5951-7
Verlag: Springer US

Buch, Englisch, Band 35, 260 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1290 g

Reihe: Nonconvex Optimization and Its Applications

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.
: 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.

Zielgruppe

Research

Autoren/Hrsg.

Haslinger, J.

Panagiotopoulos, Panagiotis D.

Miettinen, M.

Fachgebiete

• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Naturwissenschaften Physik Mechanik Klassische Mechanik, Newtonsche Mechanik
• Mathematik | Informatik Mathematik Mathematik Allgemein
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik

Inhaltsverzeichnis

I Introductory Topics.- 1. Mathematical Preliminaries.- 2. Nonsmooth Mechanics.- II Finite Element Approximation of Hemivariational Inequalities.- 3. Approximation of Elliptic Hemivariational Inequalities.- 4. Time Dependent Case.- III Nonsmooth Optimization Methods.- 5. Nonsmooth Optimization Methods.- IV Numerical Examples.- 6. Numerical Examples.