A Posteriori Error Estimation in Finite Element Analysis

A Posteriori Error Estimation in Finite Element Analysis
Title A Posteriori Error Estimation in Finite Element Analysis PDF eBook
Author Mark Ainsworth
Publisher John Wiley & Sons
Pages 266
Release 2011-09-28
Genre Mathematics
ISBN 1118031075

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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

A Posteriori Error Estimation Techniques for Finite Element Methods
Title A Posteriori Error Estimation Techniques for Finite Element Methods PDF eBook
Author Rüdiger Verfürth
Publisher Oxford University Press
Pages 414
Release 2013-04-18
Genre Mathematics
ISBN 0199679428

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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

Nonlinear Finite Element Analysis in Structural Mechanics
Title Nonlinear Finite Element Analysis in Structural Mechanics PDF eBook
Author W. Wunderlich
Publisher Springer Science & Business Media
Pages 782
Release 2013-03-14
Genre Science
ISBN 3642815898

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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

A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques

A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques
Title A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques PDF eBook
Author Rüdiger Verführt
Publisher Springer
Pages 142
Release 1996-07
Genre Mathematics
ISBN

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Adaptive Mesh Refinement - Theory and Applications

Adaptive Mesh Refinement - Theory and Applications
Title Adaptive Mesh Refinement - Theory and Applications PDF eBook
Author Tomasz Plewa
Publisher Springer Science & Business Media
Pages 550
Release 2005-12-20
Genre Mathematics
ISBN 3540270396

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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.

Finite Elements

Finite Elements
Title Finite Elements PDF eBook
Author Ivo Babuska
Publisher
Pages 336
Release 2010-11-04
Genre Mathematics
ISBN 0198506694

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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.

The Finite Element Method: Theory, Implementation, and Applications

The Finite Element Method: Theory, Implementation, and Applications
Title The Finite Element Method: Theory, Implementation, and Applications PDF eBook
Author Mats G. Larson
Publisher Springer Science & Business Media
Pages 403
Release 2013-01-13
Genre Computers
ISBN 3642332870

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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.​