A Posteriori Error Estimation For Finite Element And Generalized Finite Element Method
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Author | : Ivo Babuska |
Publisher | : |
Total Pages | : |
Release | : 1998 |
Genre | : |
ISBN | : |
Download A-posteriori error estimation for finite element and generalized finite element method Book in PDF, Epub and Kindle
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 | : 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 | : 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 | : 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 | : J. E. Akin |
Publisher | : Elsevier |
Total Pages | : 465 |
Release | : 2005-06-22 |
Genre | : Technology & Engineering |
ISBN | : 0080472753 |
Download Finite Element Analysis with Error Estimators Book in PDF, Epub and Kindle
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 |
Publisher | : |
Total Pages | : |
Release | : 1989 |
Genre | : |
ISBN | : |
Download A Posteriori Error Estimation in the Finite Element Method Book in PDF, Epub and Kindle
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 | : Varis Carey |
Publisher | : |
Total Pages | : 174 |
Release | : 2005 |
Genre | : |
ISBN | : |
Download A Posteriori Error Estimation for the Finite Element Method Via Local Averaging Book in PDF, Epub and Kindle
Author | : Gerd Kunert |
Publisher | : Logos Verlag Berlin |
Total Pages | : 0 |
Release | : 2003 |
Genre | : Finite element method |
ISBN | : 9783832504502 |
Download Advances in a Posteriori Error Estimation on Anisotropic Finite Element Discretizations Book in PDF, Epub and Kindle
Certain classes of partial differential equations generically give rise to solutions with strong directional features, e.g. with boundary layers. Such solutions are called anisotropic. Their discretization by means of the finite element method (for example) can favourably employ so-called anisotropic meshes. These meshes are characterized by stretched, anisotropic finite elements with a (very) large stretching ratio. The widespread use of computer simulation leads to an increasing demand for semi- or fully automatic solution procedures. Within such self-adaptive algorithms, a posteriori error estimators form an indispensable ingredient for quality control. They are well understood for standard, isotropic discretizations. The knowledge about a posteriori error estimation on anisotropic meshes is much less mature. During the last decade the foundation and basic principles have been proposed, discussed and established, mostly for the Poisson problem. This monograph summarises some of the recent advances in anisotropic error estimation for more challenging problems. Emphasis is given to the contributions of the author. In Chapter 3 the investigation starts with singularly perturbed reaction diffusion problems which frequently lead to solutions with boundary layers. This problem class often arises when simplifying more complex models. Chapter 4 treats singularly perturbed convection diffusion problems, i.e. the convection is dominating. The solution structure is more intricate, and often features boundary layer and/or interior layer solutions. Chapter 5 is devoted to the Stokes equations. Flow problems generically give rise to anisotropic solutions (e.g. with edge singularities or containing layers). The Stokes equations often serve as a simplified or linearised model. In all three chapters, the main results consist in error estimators and corresponding error bounds that are robust with respect to the mesh anisotropy, as far as possible. Finally Chapter 6 addresses the robustness of a posteriori error estimation with respect to the mesh anisotropy.In particular the relation between anisotropic mesh construction and error estimation is investigated. This thesis presents the philosophy of anisotropic error estimation as well as the main results and the definitions required. Proofs and technical details are omitted; instead the key ideas are explained.The compact style of presentation aims at practitioners in particular by providing easily accessible error estimators and error bounds. Further insight is readily possible through the references.