Download or read book Optimal Order Error Estimates for the Finite Element Approximation of the Solution of a Nonconvex Variational Problem written by University of Minnesota. Institute for Mathematics and Its Applications and published by . This book was released on 1990 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Enumath 97 Proceedings Of The Second European Conference On Numerical Mathematics And Advanced Applications written by Hans Georg Bock and published by World Scientific. This book was released on 1998-11-06 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: The ENUMATH conferences were established in 1995 in order to provide a forum for discussion on recent topics of numerical mathematics. They seek to bring together leading experts and young scientists, with special emphasis on contributions from Europe.In the second ENUMATH conference in 1997, recent results and new trends in the analysis of numerical algorithms as well as their application to challenging scientific and industrial problems were discussed. Apart from theoretical aspects, a major part of the conference was devoted to numerical methods in interdisciplinary applications.The topics covered in this proceedings include: higher order finite element methods, non-matching grids, least-squares methods for partial differential equations, multiscale analysis, boundary element method, optimization in partial differential equations, solid mechanics, microstructures, computational fluid dynamics, computational electrodynamics and semiconductors.
Download or read book Variational Methods in Nonlinear Elasticity written by Pablo Pedregal and published by SIAM. This book was released on 2000-01-01 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity. Pedregal introduces the reader to Young measures as an important tool in solving vector variational techniques. Readers are encouraged to pursue nonlinear elasticity as one of the best means to apply these techniques. Although there are other books devoted to nonlinear elasticity or variational methods, none are concerned with Young measures as a tool for proving existence results in nonlinear elasticity.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus Of Variations Homogenization And Continuum Mechanics written by Guy Bouchitte and published by World Scientific. This book was released on 1994-06-28 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the workshop was to promote a better understanding of the connections between recent problems in Theoretical or Computational Mechanics (bounds in composites, phase transitions, microstructure of crystals, optimal design, nonlinear elasticity) and new mathematical tools in the Calculus of Variations (relaxation and Γ-convergence theory, Young and H-measures, compensated compactness and quasiconvexity).
Download or read book Finite Element Error Analysis for PDE constrained Optimal Control Problems written by Dieter Sirch and published by Logos Verlag Berlin GmbH. This book was released on 2010 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of this work is the analysis of numerical methods for the solution of optimal control problems governed by elliptic partial differential equations. Such problems arise, if one does not only want to simulate technical or physical processes but also wants to optimize them with the help of one or more influence variables. In many practical applications these influence variables, so called controls, cannot be chosen arbitrarily, but have to fulfill certain inequality constraints. The numerical treatment of such control constrained optimal control problems requires a discretization of the underlying infinite dimensional function spaces. To guarantee the quality of the numerical solution one has to estimate and to quantify the resulting approximation errors. In this thesis a priori error estimates for finite element discretizations are proved in case of corners or edges in the underlying domain and nonsmooth coefficients in the partial differential equation. These facts influence the regularity properties of the solution and require adapted meshes to get optimal convergence rates. Isotropic and anisotropic refinement strategies are given and error estimates in polygonal and prismatic domains are proved. The theoretical results are confirmed by numerical tests.
Download or read book Applied Nonlinear Analysis written by Adélia Sequeira and published by Springer Science & Business Media. This book was released on 2007-05-08 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is meant as a present to honor Professor on the th occasion of his 70 birthday. It collects refereed contributions from sixty-one mathematicians from eleven countries. They cover many different areas of research related to the work of Professor including Navier-Stokes equations, nonlinear elasticity, non-Newtonian fluids, regularity of solutions of parabolic and elliptic problems, operator theory and numerical methods. The realization of this book could not have been made possible without the generous support of Centro de Matemática Aplicada (CMA/IST) and Fundação Calouste Gulbenkian. Special thanks are due to Dr. Ulrych for the careful preparation of the final version of this book. Last but not least, we wish to express our gratitude to Dr. for her invaluable assistance from the very beginning. This project could not have been successfully concluded without her enthusiasm and loving care for her father. On behalf of the editors ADÉLIA SEQUEIRA v honored by the Order of Merit of the Czech Republic by Václav Havel, President of the Czech Republic, on the October 28, 1998, Professor Emeritus of Mathematics at the Charles University in Prague, Presidential Research Professor at the Northern Illinois University and Doctor Honoris Causa at the Technical University of Dresden, has been enriching the Czech and world mathematics with his new ideas in the areas of partial differential equations, nonlinear functional analysis and applications of the both disciplines in continuum mechanics and hydrodynamics for more than forty years.
Download or read book Variational Methods for Discontinuous Structures written by Raul Serapioni and published by Birkhäuser. This book was released on 2012-12-06 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years many researchers in material science have focused their attention on the study of composite materials, equilibrium of crystals and crack distribution in continua subject to loads. At the same time several new issues in computer vision and image processing have been studied in depth. The understanding of many of these problems has made significant progress thanks to new methods developed in calculus of variations, geometric measure theory and partial differential equations. In particular, new technical tools have been introduced and successfully applied. For example, in order to describe the geometrical complexity of unknown patterns, a new class of problems in calculus of variations has been introduced together with a suitable functional setting: the free-discontinuity problems and the special BV and BH functions. The conference held at Villa Olmo on Lake Como in September 1994 spawned successful discussion of these topics among mathematicians, experts in computer science and material scientists.
Download or read book A Posteriori Error Estimation Techniques for Finite Element Methods written by Rüdiger Verfürth and published by OUP Oxford. This book was released on 2013-04-18 with total page 573 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Foundations of Computational Mathematics written by Ronald A. DeVore and published by Cambridge University Press. This book was released on 2001-05-17 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Collection of papers by leading researchers in computational mathematics, suitable for graduate students and researchers.
Download or read book Journal of the Society for Industrial and Applied Mathematics Series B Numerical Analysis written by Society for Industrial and Applied Mathematics and published by . This book was released on 2004 with total page 934 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Parametrized Measures and Variational Principles written by Pablo Pedregal and published by Birkhäuser. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weak convergence is a basic tool of modern nonlinear analysis because it enjoys the same compactness properties that finite dimensional spaces do: basically, bounded sequences are weak relatively compact sets. Nonetheless, weak conver gence does not behave as one would desire with respect to nonlinear functionals and operations. This difficulty is what makes nonlinear analysis much harder than would normally be expected. Parametrized measures is a device to under stand weak convergence and its behavior with respect to nonlinear functionals. Under suitable hypotheses, it yields a way of representing through integrals weak limits of compositions with nonlinear functions. It is particularly helpful in comprehending oscillatory phenomena and in keeping track of how oscilla tions change when a nonlinear functional is applied. Weak convergence also plays a fundamental role in the modern treatment of the calculus of variations, again because uniform bounds in norm for se quences allow to have weak convergent subsequences. In order to achieve the existence of minimizers for a particular functional, the property of weak lower semicontinuity should be established first. This is the crucial and most delicate step in the so-called direct method of the calculus of variations. A fairly large amount of work has been devoted to determine under what assumptions we can have this lower semicontinuity with respect to weak topologies for nonlin ear functionals in the form of integrals. The conclusion of all this work is that some type of convexity, understood in a broader sense, is usually involved.
Download or read book Relaxation in Optimization Theory and Variational Calculus written by Tomáš Roubíček and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-11-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.
Download or read book Microstructure and Phase Transition written by David Kinderlehrer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications MICROSTRUCTURE AND PHASE TRANSITION is based on the proceedings of a workshop which was an integral part of the 1990-91 IMA program on "Phase Transitions and Free Boundaries." We thank R. Fosdick, M.E. Gurtin, W.-M. Ni and L.A. Peletier for organizing the year-long program and, especially, D. Kinderlehrer, R. James, M. Luskin and J. Ericksen for organizing the meeting and editing these proceedings. We also take this opportunity to thank those agencies whose financial support made the workshop possible: the Army Research Office, and the National Science Foun dation. A vner Friedman Willard Miller. Jr. PREFACE Much of our traditional knowledge of materials and processes is achievf'd by observa tion and analysis of small departures from equilibrium. Many materials, especially modern alloys, ceramics, and their composites, experience not only larger but more dramatic changes, such as the occurrence of phase transitions and t.he creation of defect structures, when viewed at the microscopic scale. How is this observed, how can it be interpreted, and how does it influence macroscopic behavior? These are the principle concerns of this volume, which constitutes the proceedings of an IMA workshop dedicated to these issues.
Download or read book Finite Element Approximation of Variational Problems and Applications written by M. Křížek and published by Longman Scientific and Technical. This book was released on 1990 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book St Petersburg Mathematical Journal written by and published by . This book was released on 2005 with total page 718 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Analysis and Computation for a Variational Problem in Micromagnetics written by Ling Ma and published by . This book was released on 1991 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
