A Posteriori Error Estimation Techniques For Finite Element Methods
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| Author | : Rüdiger Verfürth |
| Publisher | : Oxford University Press |
| Total Pages | : 414 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 0199679428 |
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 | : W. Wunderlich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 782 |
| Release | : 2013-03-14 |
| Genre | : Science |
| ISBN | : 3642815898 |
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 | : |
| Author | : Rüdiger Verfürth |
| Publisher | : OUP Oxford |
| Total Pages | : 573 |
| Release | : 2013-04-18 |
| Genre | : Mathematics |
| ISBN | : 019166877X |
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 | : John Wiley & Sons |
| Total Pages | : 266 |
| Release | : 2011-09-28 |
| Genre | : Mathematics |
| ISBN | : 1118031075 |
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 | : Wolfgang Bangerth |
| Publisher | : Birkhäuser |
| Total Pages | : 216 |
| Release | : 2013-11-11 |
| Genre | : Mathematics |
| ISBN | : 303487605X |
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.
| Author | : Anders Logg |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 723 |
| Release | : 2012-02-24 |
| Genre | : Computers |
| ISBN | : 3642230997 |
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.
| Author | : Alexandre Ern |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 531 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 1475743556 |
This text presenting the mathematical theory of finite elements is organized into three main sections. The first part develops the theoretical basis for the finite element methods, emphasizing inf-sup conditions over the more conventional Lax-Milgrim paradigm. The second and third parts address various applications and practical implementations of the method, respectively. It contains numerous examples and exercises.
| Author | : Ivo Babuška |
| Publisher | : John Wiley & Sons |
| Total Pages | : 422 |
| Release | : 1986 |
| Genre | : Mathematics |
| ISBN | : |
This book contains papers discussing the recent developments in adaptive methods and their applications, an area of finite elements methods applicable to the needs of civil engineering. Topics covered range from an exposition of basic theory and techniques to detailed discussions of specific applications. Adaptive approaches, and the computer assessment of the reliability of the results obtained are also examined.
| Author | : P. Ladeveze |
| Publisher | : Elsevier |
| Total Pages | : 539 |
| Release | : 1998-06-23 |
| Genre | : Computers |
| ISBN | : 0080525938 |
Mastering modelling, and in particular numerical models, is becoming a crucial and central question in modern computational mechanics. Various tools, able to quantify the quality of a model with regard to another one taken as the reference, have been derived. Applied to computational strategies, these tools lead to new computational methods which are called "adaptive". The present book is concerned with outlining the state of the art and the latest advances in both these important areas.Papers are selected from a Workshop (Cachan 17-19 September 1997) which is the third of a series devoted to Error Estimators and Adaptivity in Computational Mechanics. The Cachan Workshop dealt with latest advances in adaptive computational methods in mechanics and their impacts on solving engineering problems. It was centered too on providing answers to simple questions such as: what is being used or can be used at present to solve engineering problems? What should be the state of art in the year 2000? What are the new questions involving error estimators and their applications?
