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Adaptive Error Control In The Finite Element Method For Time Dependent Problems
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Book Synopsis Adaptive Finite Element Methods for Differential Equations by : Wolfgang Bangerth
Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Book Synopsis Error-controlled Adaptive Finite Elements in Solid Mechanics by : Ekkehard Ramm
Download or read book Error-controlled Adaptive Finite Elements in Solid Mechanics written by Ekkehard Ramm and published by John Wiley & Sons. This book was released on 2002-12-30 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. First book to go beyond the Finite Element Method in itself Covers material from a new research area Presents benchmarks of 2D- and 3D- applications Fits with the new trend for genetic strategies in engineering
Book Synopsis Acta Numerica 1995: Volume 4 by : Arieh Iserles
Download or read book Acta Numerica 1995: Volume 4 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1995-07-13 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.
Book Synopsis Adaptive Finite Elements in the Discretization of Parabolic Problems by : Christian A. Möller
Download or read book Adaptive Finite Elements in the Discretization of Parabolic Problems written by Christian A. Möller and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Adaptivity is a crucial tool in state-of-the-art scientific computing. However, its theoretical foundations are only understood partially and are subject of current research. This self-contained work provides theoretical basics on partial differential equations and finite element discretizations before focusing on adaptive finite element methods for time dependent problems. In this context, aspects of temporal adaptivity and error control are considered in particular. Based on the gained insights, a specific adaptive algorithm is designed and analyzed thoroughly. Most importantly, it is proven that the presented adaptive method terminates within any demanded error tolerance. Moreover, the developed algorithm is analyzed from a numerical point of view and its performance is compared to well-known standard methods. Finally, it is applied to the real-life problem of concrete carbonation, where two different discretizations are compared.
Book Synopsis Acta Numerica 2001: Volume 10 by : Arieh Iserles
Download or read book Acta Numerica 2001: Volume 10 written by Arieh Iserles and published by Cambridge University Press. This book was released on 2001-08-23 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: An annual volume presenting substantive survey articles in numerical analysis and scientific computing.
Book Synopsis A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques by : Rüdiger Verführt
Download or read book A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques written by Rüdiger Verführt and published by Springer. This book was released on 1996-07 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Posteriori Error Estimation Techniques for Finite Element Methods by : Rüdiger Verfürth
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 414 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.
Book Synopsis Advances in Adaptive Computational Methods in Mechanics by : P. Ladeveze
Download or read book Advances in Adaptive Computational Methods in Mechanics written by P. Ladeveze and published by Elsevier. This book was released on 1998-06-23 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mastering modelling, and in particular numerical models, is becoming a crucial and central question in modern computational mechanics. Various tools, able to quantify the quality of a model with regard to another one taken as the reference, have been derived. Applied to computational strategies, these tools lead to new computational methods which are called "adaptive". The present book is concerned with outlining the state of the art and the latest advances in both these important areas.Papers are selected from a Workshop (Cachan 17-19 September 1997) which is the third of a series devoted to Error Estimators and Adaptivity in Computational Mechanics. The Cachan Workshop dealt with latest advances in adaptive computational methods in mechanics and their impacts on solving engineering problems. It was centered too on providing answers to simple questions such as: what is being used or can be used at present to solve engineering problems? What should be the state of art in the year 2000? What are the new questions involving error estimators and their applications?
Book Synopsis Error Control and Adaptivity in Scientific Computing by : Haydar Bulgak
Download or read book Error Control and Adaptivity in Scientific Computing written by Haydar Bulgak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.
Book Synopsis Numerical Methods for Fluid Dynamics V by : K. W. Morton
Download or read book Numerical Methods for Fluid Dynamics V written by K. W. Morton and published by Oxford University Press. This book was released on 1995 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of an international conference on Numerical Methods for Fluid Dynamics held at the University of Oxford in April 1995. It provides a summary of recent research on the computational aspects of fluid dynamics. It includes contributions from many distinguished mathematicians and engineers and, as always, the standard of papers is high. The main themes of the book are algorithms and algorithmic needs arising from applications, Navier-Stokes on flexible grids, and environmental computational fluid dynamics. Graduate students of numerical analysis will find the up-to-date coverage of research in this book very useful.
Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Book Synopsis Enumath 97 - Proceedings Of The Second European Conference On Numerical Mathematics And Advanced Applications by : Hans Georg Bock
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.
Book Synopsis Control and Boundary Analysis by : John Cagnol
Download or read book Control and Boundary Analysis written by John Cagnol and published by CRC Press. This book was released on 2005-03-04 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises selected papers from the 21st Conference on System Modeling and Optimization in Sophia Antipolis, France. It covers over three decades of studies involving partial differential systems and equations. Topics include: the modeling of continuous mechanics involving fixed boundary, control theory, shape optimization and moving bou
Book Synopsis Space-Time Methods by : Ulrich Langer
Download or read book Space-Time Methods written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-09-23 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an introduction to modern space-time discretization methods such as finite and boundary elements and isogeometric analysis for time-dependent initial-boundary value problems of parabolic and hyperbolic type. Particular focus is given on stable formulations, error estimates, adaptivity in space and time, efficient solution algorithms, parallelization of the solution pipeline, and applications in science and engineering.
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:
Book Synopsis Inverse Problems and Applications by : Larisa Beilina
Download or read book Inverse Problems and Applications written by Larisa Beilina and published by Springer. This book was released on 2015-02-17 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume arose from the Third Annual Workshop on Inverse Problems, held in Stockholm on May 2-6, 2012. The proceedings present new analytical developments and numerical methods for solutions of inverse and ill-posed problems, which consistently pose complex challenges to the development of effective numerical methods. The book highlights recent research focusing on reliable numerical techniques for the solution of inverse problems, with relevance to a range of fields including acoustics, electromagnetics, optics, medical imaging, and geophysics.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
