A Posteriori Error Estimation In Finite Element Analysis
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| Author | : Mark Ainsworth |
| Publisher | : John Wiley & Sons |
| Total Pages | : 266 |
| Release | : 2011-09-28 |
| Genre | : Mathematics |
| ISBN | : 1118031075 |
Download A Posteriori Error Estimation in Finite Element Analysis Book in PDF, Epub and Kindle
An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.
| Author | : Rüdiger Verfürth |
| Publisher | : Oxford University Press |
| Total Pages | : 414 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 0199679428 |
Download A Posteriori Error Estimation Techniques for Finite Element Methods Book in PDF, Epub and Kindle
A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.
| Author | : Mark Ainsworth |
| Publisher | : |
| Total Pages | : |
| Release | : 1996 |
| Genre | : |
| ISBN | : |
Download A posteriori error estimation in finite element analysis Book in PDF, Epub and Kindle
| Author | : Rüdiger Verfürth |
| Publisher | : OUP Oxford |
| Total Pages | : 573 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 019166877X |
Download A Posteriori Error Estimation Techniques for Finite Element Methods Book in PDF, Epub and Kindle
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.
| Author | : Ivo Babuska |
| Publisher | : |
| Total Pages | : 336 |
| Release | : 2010-11-04 |
| Genre | : Mathematics |
| ISBN | : 0198506694 |
Download Finite Elements Book in PDF, Epub and Kindle
Most of the many books on finite elements are devoted either to mathematical theory or to engineering applications, but not to both. This book presents computed numbers which not only illustrate the theory but can only be analysed using the theory. This approach, both dual and interacting between theory and computation makes this book unique.
| Author | : W. Wunderlich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 782 |
| Release | : 2013-03-14 |
| Genre | : Science |
| ISBN | : 3642815898 |
Download Nonlinear Finite Element Analysis in Structural Mechanics Book in PDF, Epub and Kindle
With the rap1d development of computational capab1lities, nonl1near f1nite element analys1s 1n structural mechan1CS has become an 1mportant field of research. Its objective is the real1stic assessment of the actual behaV10r of structures by numerical methods. Th1S requires that all nonlinear effects, such as the nonl1near character1stics of the mater1al and large deformations be taken 1nto account. The act1vities in th1S f1eld be1ng worldw1de, d1rect 1nteraction between the various research groups 1S necessary to coordinate future research and to overcome the time gap between the generat10n of new results and the1r appearance 1n the 11terature. The f1rst U.S.-Germany Sympos1um was held 1n 1976 at the Massachusetts Inst1tute of Technology. Under the general to P1C "Formulat1ons and Computat1onal Algorithms in Fin1te Ele ment Analysis" 1t prov1ded an opportun1ty for about 20 re searchers from each country to present lectures, hold discus sions, and establ1sh mutual contacts. The success of th1S first sympos1um was so encourag1ng that 1t seemed natural to organ- 1ze a second bilateral meet1ng, this time 1n Germany, and to 1nv1te researchers from other European countr1es as well
| Author | : Rüdiger Verführt |
| Publisher | : Springer |
| Total Pages | : 142 |
| Release | : 1996-07 |
| Genre | : Mathematics |
| ISBN | : |
Download A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Book in PDF, Epub and Kindle
| Author | : Tomasz Plewa |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 550 |
| Release | : 2005-12-20 |
| Genre | : Mathematics |
| ISBN | : 3540270396 |
Download Adaptive Mesh Refinement - Theory and Applications Book in PDF, Epub and Kindle
Advanced numerical simulations that use adaptive mesh refinement (AMR) methods have now become routine in engineering and science. Originally developed for computational fluid dynamics applications these methods have propagated to fields as diverse as astrophysics, climate modeling, combustion, biophysics and many others. The underlying physical models and equations used in these disciplines are rather different, yet algorithmic and implementation issues facing practitioners are often remarkably similar. Unfortunately, there has been little effort to review the advances and outstanding issues of adaptive mesh refinement methods across such a variety of fields. This book attempts to bridge this gap. The book presents a collection of papers by experts in the field of AMR who analyze past advances in the field and evaluate the current state of adaptive mesh refinement methods in scientific computing.
| Author | : Pedro Díez |
| Publisher | : |
| Total Pages | : 20 |
| Release | : 1995 |
| Genre | : Finite element method |
| ISBN | : |
Download A Posteriori Error Estimation for Standard Finite Element Analysis Book in PDF, Epub and Kindle
| Author | : Barna Szabó |
| Publisher | : John Wiley & Sons |
| Total Pages | : 337 |
| Release | : 2011-03-21 |
| Genre | : Technology & Engineering |
| ISBN | : 1119993482 |
Download Introduction to Finite Element Analysis Book in PDF, Epub and Kindle
When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort. Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout. Delivers the tools needed to have a working knowledge of the finite element method Illustrates the concepts and procedures of verification and validation Explains the process of conceptualization supported by virtual experimentation Describes the convergence characteristics of the h-, p- and hp-methods Covers the hierarchic view of mathematical models and finite element spaces Uses examples and exercises which illustrate the techniques and procedures of quality assurance Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians Includes parameter-controlled examples of solved problems in a companion website (www.wiley.com/go/szabo)
