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.
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First Sentence:
In order to keep the presentation as self-contained we decided to start with basic results, which will be needed in subsequent parts of the monograph. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constrained hemivariational inequality, metric bundle methods, proximal bundle method, parabolic hemivariational inequalities, evolution triplet, direction finding problem, parabolic variational inequality, linearization error, contact nodes, locality measure, subgradient methods, nondifferentiable optimization, nonsmooth optimization, nonconvex case, generalized directional derivative, following convergence result, cutting plane method, polygonal domain, unconstrained case, numerical realization, nonconvex optimization, inverse inequality, friction law, deletion rules, convex functional Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, North Holland, Academic Press, Marcel Dekker New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In order to keep the presentation as self-contained we decided to start with basic results, which will be needed in subsequent parts of the monograph. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
constrained hemivariational inequality, metric bundle methods, proximal bundle method, parabolic hemivariational inequalities, evolution triplet, direction finding problem, parabolic variational inequality, linearization error, contact nodes, locality measure, subgradient methods, nondifferentiable optimization, nonsmooth optimization, nonconvex case, generalized directional derivative, following convergence result, cutting plane method, polygonal domain, unconstrained case, numerical realization, nonconvex optimization, inverse inequality, friction law, deletion rules, convex functional Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, North Holland, Academic Press, Marcel Dekker New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 24
books:
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- Numerical Methods for Nonlinear Variational Problems (Scientific Computation) by Roland Glowinski on page 81, page 161, and page 200
- Functional Analysis (Springer Classics in Mathematics) by Kosaku Yosida on page 82, and page 228
- The Finite Element Method for Elliptic Problems (Classics in Applied Mathematics) by Philippe G. Ciarlet on page 81, and page 161
- System Modelling and Optimization (IFIP Advances in Information and Communication Technology) by J. Dolezal on page 225
- Finite Element Methods: Lecture Notes in Pure and Applied Mathematics, Vol 196 by Michel Krizek on page 82
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