Finite Element Analysis With Error Estimators

Author : J. E. Akin
Publisher : Elsevier
Page : 465 pages
File Size : 43,6 Mb
Release : 2005-06-22
Category : Technology & Engineering
ISBN : 9780080472751

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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

Author : Mark Ainsworth,J. Tinsley Oden
Publisher : John Wiley & Sons
Page : 266 pages
File Size : 45,9 Mb
Release : 2011-09-28
Category : Mathematics
ISBN : 9781118031070

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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.

Author : Rudiger Verfurth,Rüdiger Verfürth
Publisher : Oxford University Press
Page : 414 pages
File Size : 55,6 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780199679423

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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.

Author : Ivo Babuska,John Whiteman,Theofanis Strouboulis
Publisher : Unknown
Page : 336 pages
File Size : 53,9 Mb
Release : 2010-11-04
Category : Mathematics
ISBN : 9780198506690

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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.

Author : Mark Ainsworth
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 1996
Category : Electronic
ISBN : OCLC:122295041

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A posteriori error estimation in finite element analysis by Mark Ainsworth Pdf

Author : W. Wunderlich,E. Stein,K.J. Bathe
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 52,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783642815898

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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

Author : Barna Szabó,Ivo Babuška
Publisher : John Wiley & Sons
Page : 408 pages
File Size : 53,8 Mb
Release : 1991-09-03
Category : Technology & Engineering
ISBN : 0471502731

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Finite Element Analysis by Barna Szabó,Ivo Babuška Pdf

Covers the fundamentals of linear theory of finite elements, from both mathematical and physical points of view. Major focus is on error estimation and adaptive methods used to increase the reliability of results. Incorporates recent advances not covered by other books.

Author : Michel Krizek
Publisher : Routledge
Page : 275 pages
File Size : 40,8 Mb
Release : 2017-11-22
Category : Mathematics
ISBN : 9781351448604

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Finite Element Methods by Michel Krizek Pdf

""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.

Author : Olek C Zienkiewicz,Robert L. Taylor,J.Z. Zhu
Publisher : Elsevier
Page : 753 pages
File Size : 48,7 Mb
Release : 2005-05-26
Category : Technology & Engineering
ISBN : 9780080472775

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The Finite Element Method: Its Basis and Fundamentals by Olek C Zienkiewicz,Robert L. Taylor,J.Z. Zhu Pdf

The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics. The classic introduction to the finite element method, by two of the subject's leading authors Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text

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

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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.

Author : Rüdiger Verführt
Publisher : Springer
Page : 142 pages
File Size : 50,7 Mb
Release : 1996-07
Category : Mathematics
ISBN : CORNELL:31924084448004

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A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques by Rüdiger Verführt Pdf

Author : Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu
Publisher : Butterworth-Heinemann
Page : 756 pages
File Size : 47,6 Mb
Release : 2013-08-31
Category : Technology & Engineering
ISBN : 9780080951355

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The Finite Element Method: Its Basis and Fundamentals by Olek C Zienkiewicz,Robert L Taylor,J.Z. Zhu Pdf

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development. Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience. Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.

Author : Rüdiger Verfürth
Publisher : OUP Oxford
Page : 416 pages
File Size : 49,8 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780191668760

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

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 : John O. Dow
Publisher : Momentum Press
Page : 271 pages
File Size : 44,9 Mb
Release : 2012-07-01
Category : Technology & Engineering
ISBN : 9781606503348

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The Essentials of Finite Element Modeling and Adaptive Refinement by John O. Dow Pdf

Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh. " The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool. The book presents * A more simplified approach to finite element analysis based on computational continuum mechanics * Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics

Author : Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich
Publisher : John Wiley & Sons
Page : 422 pages
File Size : 45,9 Mb
Release : 2003-08-01
Category : Technology & Engineering
ISBN : 9780470857977

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Error-controlled Adaptive Finite Elements in Solid Mechanics by Ekkehard Ramm,E. Rank,R. Rannacher,K. Schweizerhof,E. Stein,W. Wendland,G. Wittum,Peter Wriggers,Walter Wunderlich Pdf

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