A Posteriori Error Estimation In The Finite Element Method
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A Posteriori Error Estimation In Finite Element Analysis
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Author : Mark Ainsworth
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-28
A Posteriori Error Estimation In Finite Element Analysis written by Mark Ainsworth and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.
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
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Author : Rüdiger Verfürth
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
A Posteriori Error Estimation Techniques For Finite Element Methods written by Rüdiger Verfürth and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
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.
A Posteriori Error Estimation In The Finite Element Method
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Author : Mark Ainsworth
language : en
Publisher:
Release Date : 1989
A Posteriori Error Estimation In The Finite Element Method written by Mark Ainsworth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
A Posteriori Error Estimation In Finite Element Analysis
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Author : Mark Ainsworth
language : en
Publisher:
Release Date : 1996
A Posteriori Error Estimation In Finite Element Analysis written by Mark Ainsworth and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
A Posteriori Error Estimation For The Finite Element Method Via Local Averaging
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Author : Varis Carey
language : en
Publisher:
Release Date : 2005
A Posteriori Error Estimation For The Finite Element Method Via Local Averaging written by Varis Carey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
A Feedback Finite Element Method With A Posteriori Error Estimation
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Author : I. Babuska
language : en
Publisher:
Release Date : 1984
A Feedback Finite Element Method With A Posteriori Error Estimation written by I. Babuska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Finite element method categories.
This paper is the first in a series of three which discusses some theoretical and practical aspect of a feedback finite element method for solving systems of linear second order elliptic partial differential equations (with particular interest in classical linear elasticity). This first part introduces some nonstandard finite element spaces, though based on the usual square bilinear elements, permit local mesh refinement. The algebraic structure of these spaces and their approximation properties are analysed. An equivalent estimator for the H1 finite element error is developed.
Advances In A Posteriori Error Estimation On Anisotropic Finite Element Discretizations
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Author : Gerd Kunert
language : en
Publisher: Logos Verlag Berlin
Release Date : 2003
Advances In A Posteriori Error Estimation On Anisotropic Finite Element Discretizations written by Gerd Kunert and has been published by Logos Verlag Berlin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Finite element method categories.
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.
A Posteriori Error Estimation In A Finite Element Method For Parabolic Partial Differential Equations
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Author : J. M. Coyle
language : en
Publisher:
Release Date : 1987
A Posteriori Error Estimation In A Finite Element Method For Parabolic Partial Differential Equations written by J. M. Coyle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Superconvergence properties and quadratic polynomials are used to derive a computationally inexpensive approximation to the spatial component of the error in a piecewise linear finite element method for one-dimensional parabolic partial differential equations. This technique is coupled with time integration schemes of successively higher orders to obtain an approximation of the temporal and total discretization errors. Computational results indicate that these approximations converge to the exact discretization errors as the mesh is refined. The approximate errors are used to control an adaptive mesh refinement strategy. Keywords: Trapezoidal rule; Galerkins method.
Nonlinear Finite Element Analysis In Structural Mechanics
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Author : W. Wunderlich
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Finite Element Analysis In Structural Mechanics written by W. Wunderlich and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
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 Feedback Finite Element Method And Some Basic Properties Of The A Posteriori Error Estimation
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Author : Ivo Babuska
language : en
Publisher:
Release Date : 1984
A Feedback Finite Element Method And Some Basic Properties Of The A Posteriori Error Estimation written by Ivo Babuska and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.