A Posteriori Error Estimation In Finite Element Analysis

A Posteriori Error Estimation In Finite Element Analysis Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of A Posteriori Error Estimation In Finite Element Analysis book. This book definitely worth reading, it is an incredibly well-written.

A Posteriori Error Estimation in Finite Element Analysis

Mark Ainsworth,J. Tinsley Oden
A Posteriori Error Estimation in Finite Element Analysis Book PDF

Author : Mark Ainsworth,J. Tinsley Oden
Publisher : John Wiley & Sons
Page : 266 pages
File Size : 48,5 Mb
Release : 2011-09-28
Category : Mathematics
ISBN : 9781118031070

Get Book

A Posteriori Error Estimation in Finite Element Analysis by Mark Ainsworth,J. Tinsley Oden Pdf

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.

A Posteriori Error Estimation Techniques for Finite Element Methods

Rudiger Verfurth,Rüdiger Verfürth
A Posteriori Error Estimation Techniques for Finite Element Methods Book PDF

Author : Rudiger Verfurth,Rüdiger Verfürth
Publisher : Oxford University Press
Page : 414 pages
File Size : 54,9 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780199679423

Get Book

A Posteriori Error Estimation Techniques for Finite Element Methods by Rudiger Verfurth,Rüdiger Verfürth Pdf

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.

Nonlinear Finite Element Analysis in Structural Mechanics

W. Wunderlich,E. Stein,K.J. Bathe
Nonlinear Finite Element Analysis in Structural Mechanics Book PDF

Author : W. Wunderlich,E. Stein,K.J. Bathe
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 45,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783642815898

Get Book

Nonlinear Finite Element Analysis in Structural Mechanics by W. Wunderlich,E. Stein,K.J. Bathe Pdf

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

Finite Element Analysis with Error Estimators

J. E. Akin
Finite Element Analysis with Error Estimators Book PDF

Author : J. E. Akin
Publisher : Elsevier
Page : 465 pages
File Size : 40,9 Mb
Release : 2005-06-22
Category : Technology & Engineering
ISBN : 9780080472751

Get Book

Finite Element Analysis with Error Estimators by J. E. Akin Pdf

This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators

Finite Elements

Ivo Babuska,John Whiteman,Theofanis Strouboulis
Finite Elements Book PDF

Author : Ivo Babuska,John Whiteman,Theofanis Strouboulis
Publisher : Unknown
Page : 336 pages
File Size : 50,5 Mb
Release : 2010-11-04
Category : Mathematics
ISBN : 9780198506690

Get Book

Finite Elements by Ivo Babuska,John Whiteman,Theofanis Strouboulis Pdf

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.

Adaptive Mesh Refinement - Theory and Applications

Tomasz Plewa,Timur Linde,V. Gregory Weirs
Adaptive Mesh Refinement Theory and Applications Book PDF

Author : Tomasz Plewa,Timur Linde,V. Gregory Weirs
Publisher : Springer Science & Business Media
Page : 550 pages
File Size : 43,7 Mb
Release : 2005-12-20
Category : Mathematics
ISBN : 9783540270393

Get Book

Adaptive Mesh Refinement - Theory and Applications by Tomasz Plewa,Timur Linde,V. Gregory Weirs Pdf

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.

The Finite Element Method: Theory, Implementation, and Applications

Mats G. Larson,Fredrik Bengzon
The Finite Element Method Theory Implementation and Applications Book PDF

Author : Mats G. Larson,Fredrik Bengzon
Publisher : Springer Science & Business Media
Page : 403 pages
File Size : 55,9 Mb
Release : 2013-01-13
Category : Computers
ISBN : 9783642332876

Get Book

The Finite Element Method: Theory, Implementation, and Applications by Mats G. Larson,Fredrik Bengzon Pdf

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Adaptive Finite Element Methods for Differential Equations

Wolfgang Bangerth,Rolf Rannacher
Adaptive Finite Element Methods for Differential Equations Book PDF

Author : Wolfgang Bangerth,Rolf Rannacher
Publisher : Birkhäuser
Page : 216 pages
File Size : 47,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783034876056

Get Book

Adaptive Finite Element Methods for Differential Equations by Wolfgang Bangerth,Rolf Rannacher Pdf

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.

Introduction to Finite Element Analysis

Barna Szabó,Ivo Babuška
Introduction to Finite Element Analysis Book PDF

Author : Barna Szabó,Ivo Babuška
Publisher : John Wiley & Sons
Page : 337 pages
File Size : 47,6 Mb
Release : 2011-03-21
Category : Technology & Engineering
ISBN : 9781119993483

Get Book

Introduction to Finite Element Analysis by Barna Szabó,Ivo Babuška Pdf

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)

The Finite Element Method and Its Reliability

Ivo Babuška,Theofanis Strouboulis
The Finite Element Method and Its Reliability Book PDF

Author : Ivo Babuška,Theofanis Strouboulis
Publisher : Oxford University Press
Page : 820 pages
File Size : 42,7 Mb
Release : 2001
Category : Mathematics
ISBN : 0198502761

Get Book

The Finite Element Method and Its Reliability by Ivo Babuška,Theofanis Strouboulis Pdf

The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.

Automated Solution of Differential Equations by the Finite Element Method

Anders Logg,Kent-Andre Mardal,Garth Wells
Automated Solution of Differential Equations by the Finite Element Method Book PDF

Author : Anders Logg,Kent-Andre Mardal,Garth Wells
Publisher : Springer Science & Business Media
Page : 723 pages
File Size : 48,7 Mb
Release : 2012-02-24
Category : Computers
ISBN : 9783642230998

Get Book

Automated Solution of Differential Equations by the Finite Element Method by Anders Logg,Kent-Andre Mardal,Garth Wells Pdf

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.