Regularization Methods And Finite Element Approximation Of Hemivariational Inequalities With Applications To Nonmonotone Contact Problems
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Regularization Methods And Finite Element Approximation Of Hemivariational Inequalities With Applications To Nonmonotone Contact Problems
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Author : Nina Ovcharova
language : en
Publisher: Cuvillier Verlag
Release Date : 2012-09-11
Regularization Methods And Finite Element Approximation Of Hemivariational Inequalities With Applications To Nonmonotone Contact Problems written by Nina Ovcharova and has been published by Cuvillier Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
In this thesis, we consider mechanical problems with nonmonotone contact, like adhesive problems, delamination problems, bilateral contact problems with nonmonotone friction law, nonmonotone unilateral contact, etc. In all of them the contact phenomena are described by nonmonotone and multivalued laws, which can be expressed by means of the Clarke subdifferential of a locally Lipschitz function called a nonconvex, nonsmooth superpotential. Problems involving such laws give rise to hemivariational inequalities introduced for the first time by the engineer Panagiotopoulos in the eighties. In this work, we combine the regularization techniques with the finite element method to approximate a special class of hemivariational inequalities with maximum (resp. minimum) superpotential. Using some classes of smoothing approximations for nonsmooth functions based on convolution, we provide a regularization procedure to smooth the nonsmooth superpotential. The non-differentiable functional is approximated by a family of differentiable ones. Convergence of the solution based on the regularized problem to the solution of the original problem is shown. Then, the finite element approach for the regularized problem is analysed and convergence results are given. As an application we consider some model examples from continuum mechanics with nonmonotone contact and present some numerical results.
Optimization In Science And Engineering
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-05-29
Optimization In Science And Engineering written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-29 with Mathematics categories.
Optimization in Science and Engineering is dedicated in honor of the 60th birthday of Distinguished Professor Panos M. Pardalos. Pardalos’s past and ongoing work has made a significant impact on several theoretical and applied areas in modern optimization. As tribute to the diversity of Dr. Pardalos’s work in Optimization, this book comprises a collection of contributions from experts in various fields of this rich and diverse area of science. Topics highlight recent developments and include: Deterministic global optimization Variational inequalities and equilibrium problems Approximation and complexity in numerical optimization Non-smooth optimization Statistical models and data mining Applications of optimization in medicine, energy systems, and complex network analysis This volume will be of great interest to graduate students, researchers, and practitioners, in the fields of optimization and engineering.
Constructive Nonsmooth Analysis And Related Topics
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Author : Vladimir F. Demyanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-12
Constructive Nonsmooth Analysis And Related Topics written by Vladimir F. Demyanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-12 with Mathematics categories.
This volume contains a collection of papers based on lectures and presentations delivered at the International Conference on Constructive Nonsmooth Analysis (CNSA) held in St. Petersburg (Russia) from June 18-23, 2012. This conference was organized to mark the 50th anniversary of the birth of nonsmooth analysis and nondifferentiable optimization and was dedicated to J.-J. Moreau and the late B.N. Pshenichnyi, A.M. Rubinov, and N.Z. Shor, whose contributions to NSA and NDO remain invaluable. The first four chapters of the book are devoted to the theory of nonsmooth analysis. Chapters 5-8 contain new results in nonsmooth mechanics and calculus of variations. Chapters 9-13 are related to nondifferentiable optimization, and the volume concludes with four chapters containing interesting and important historical chapters, including tributes to three giants of nonsmooth analysis, convexity, and optimization: Alexandr Alexandrov, Leonid Kantorovich, and Alex Rubinov. The last chapter provides an overview and important snapshots of the 50-year history of convex analysis and optimization.
Advanced Boundary Element Methods
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Author : Joachim Gwinner
language : en
Publisher: Springer
Release Date : 2018-07-28
Advanced Boundary Element Methods written by Joachim Gwinner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-28 with Mathematics categories.
This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods – efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.
Applied Mathematics In Tunisia
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Author : Aref Jeribi
language : en
Publisher: Birkhäuser
Release Date : 2015-10-05
Applied Mathematics In Tunisia written by Aref Jeribi and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-05 with Mathematics categories.
This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2004
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
Nonsmooth Mechanics And Applications
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Author : J.J. Moreau
language : en
Publisher: Springer
Release Date : 2014-05-04
Nonsmooth Mechanics And Applications written by J.J. Moreau and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.
Regularization Algorithms For Ill Posed Problems
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Author : Anatoly B. Bakushinsky
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-02-05
Regularization Algorithms For Ill Posed Problems written by Anatoly B. Bakushinsky and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
This specialized and authoritative book contains an overview of modern approaches to constructing approximations to solutions of ill-posed operator equations, both linear and nonlinear. These approximation schemes form a basis for implementable numerical algorithms for the stable solution of operator equations arising in contemporary mathematical modeling, and in particular when solving inverse problems of mathematical physics. The book presents in detail stable solution methods for ill-posed problems using the methodology of iterative regularization of classical iterative schemes and the techniques of finite dimensional and finite difference approximations of the problems under study. Special attention is paid to ill-posed Cauchy problems for linear operator differential equations and to ill-posed variational inequalities and optimization problems. The readers are expected to have basic knowledge in functional analysis and differential equations. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems, and also to advanced students in these fields. Contents Introduction Regularization Methods For Linear Equations Finite Difference Methods Iterative Regularization Methods Finite-Dimensional Iterative Processes Variational Inequalities and Optimization Problems
Regularization For Applied Inverse And Ill Posed Problems
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Author :
language : de
Publisher: Springer-Verlag
Release Date : 2013-11-22
Regularization For Applied Inverse And Ill Posed Problems written by and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-22 with Technology & Engineering categories.
A Posteriori Error Estimation Techniques For Finite Element Methods
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Author : Rüdiger Verfürth
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
A Posteriori Error Estimation Techniques For Finite Element Methods written by Rüdiger Verfürth and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.