A Review Of Posteriori Error Estimation Adaptive Mesh Refinement Techniques
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A Review Of Posteriori Error Estimation Adaptive Mesh Refinement Techniques
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Author : Rudiger Verfurth
language : en
Publisher: Wiley
Release Date : 1996-06-11
A Review Of Posteriori Error Estimation Adaptive Mesh Refinement Techniques written by Rudiger Verfurth and has been published by Wiley this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-11 with Mathematics categories.
Wiley—Teubner Series Advances in Numerical Mathematics Editors Hans Georg Bock Mitchell Luskin Wolfgang Hackbusch Rolf Rannacher A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques Rüdiger Verfürth Ruhr-Universität Bochum, Germany Self-adaptive discretization methods have gained an enormous importance for the numerical solution of partial differential equations which arise in physical and technical applications. The aim of these methods is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools utilised are a posteriori error estimators and indicators which are able to give global and local information on the error of the numerical solution, using only the computed numerical solution and known data of the problem. Presenting the most frequently used error estimators which have been developed by various scientists in the last two decades, this book demonstrates that they are all based on the same basic principles. These principles are then used to develop an abstract framework which is able to handle general nonlinear problems. The abstract results are applied to various classes of nonlinear elliptic partial differential equations from, for example, fluid and continuum mechanics, to yield reliable and easily computable error estimators. The book covers stationary problems but omits transient problems, where theory is often still too complex and not yet well developed.
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques
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Author : Rüdiger Verführt
language : en
Publisher: Springer
Release Date : 1996-07
A Review Of A Posteriori Error Estimation And Adaptive Mesh Refinement Techniques written by Rüdiger Verführt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07 with Mathematics categories.
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.
The Finite Element Method Its Basis And Fundamentals
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Author : Olek C Zienkiewicz
language : en
Publisher: Elsevier
Release Date : 2005-05-26
The Finite Element Method Its Basis And Fundamentals written by Olek C Zienkiewicz and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-26 with Technology & Engineering categories.
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
Adaptive Mesh Refinement Based On A Posteriori Error Estimation
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Author : Martin Juhas
language : en
Publisher:
Release Date : 2014
Adaptive Mesh Refinement Based On A Posteriori Error Estimation written by Martin Juhas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with categories.
Goal Oriented A Posteriori Error Estimation And Adaptive Mesh Refinement In 2d 3d Thermoelasticity Problems
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Author : Ehsan Rabizadeh
language : en
Publisher:
Release Date : 2019
Goal Oriented A Posteriori Error Estimation And Adaptive Mesh Refinement In 2d 3d Thermoelasticity Problems written by Ehsan Rabizadeh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
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.
Adaptive Mesh Refinement Theory And Applications
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Author : Tomasz Plewa
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-20
Adaptive Mesh Refinement Theory And Applications written by Tomasz Plewa 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 2005-12-20 with Mathematics categories.
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.
A Posteriori Error Estimation For Finite Element Approximations Of Fractional Laplacian Problems And Applications To Poro Elasticity
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Author : Raphaël Bulle
language : en
Publisher:
Release Date : 2022
A Posteriori Error Estimation For Finite Element Approximations Of Fractional Laplacian Problems And Applications To Poro Elasticity written by Raphaël Bulle and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.
This manuscript is concerned with a posteriori error estimation for the finiteelement discretization of standard and fractional partial differential equationsas well as an application of fractional calculus to the modeling of thehuman meniscus by poro-elasticity equations.In the introduction, we give an overview of the literature about a posteriori errorestimation for finite element methods and about adaptive mesh refinement methods.We also review the literature about fractional partial differential equationsand Caputo's fractional derivative with anomalous diffusion applications.We emphasize on the state-of-the-art of the Bank-Weiser estimator and of aposteriori error estimation for the spectral fractional Laplacian.The rest of the manuscript is organized as follows.The Chapter 1 is concerned with a proof of the reliability of theBank-Weiser estimator for three-dimensional problems discretized with linearLagrange finite elements. This result is an extension of a previous result fromthe literature.In Chapter 2 we present a numerical study of the Bank-Weiserestimator.We provide a novel implementation of the estimator in the FEniCS finiteelement software and working in parallel.We apply our code to a variety of elliptic equations, several differenttwo-dimensional Poisson problems and a three-dimensional linear elasticityproblem.In particular, we use our implementation into an adaptive mesh refinement method anda goal-oriented error estimation method.In addition we provide convergence studies for these methods as well as atimescale study of our error estimation method when performed in parallel.In Chapter 3 we derive a novel a posteriori estimator for theL2 error induced by the finite element discretization of the fractionalLaplacian operator.We provide an implementation of our method in the FEniCS finite elementsoftware.We apply our estimator to an adaptive refinement method for two-dimensional andthree-dimensional fractional Poisson equations.In addition, we provide numerical results on the convergence of this method.In Chapter 4 we present new theoretical results on theconvergence of a rational approximation method with consequences on theapproximation of fractional norms and a priori error estimation of the semi-discretization of the spectral fractional Laplacian.Finally, in Chapter 5 we provide an application of fractionalcalculus to the study of the human meniscus via poro-elasticity equations and the Caputo derivative.
An A Posteriori Error Estimator For Adaptive Mesh Refinement Using Parallel In Element Particle Tracking Methods
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Author :
language : en
Publisher:
Release Date : 2003
An A Posteriori Error Estimator For Adaptive Mesh Refinement Using Parallel In Element Particle Tracking Methods written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Differential equations, Partial categories.