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Author : Rüdiger Verführt
Publisher : Springer
Page : 142 pages
File Size : 47,8 Mb
Release : 1996-07
Category : Mathematics
ISBN : CORNELL:31924084448004
Author : Rudiger Verfurth
Publisher : Wiley
Page : 134 pages
File Size : 49,5 Mb
Release : 1996-06-11
Category : Mathematics
ISBN : 0471967955
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.
Author : Olek C Zienkiewicz,Robert L. Taylor,J.Z. Zhu
Publisher : Elsevier
Page : 753 pages
File Size : 47,6 Mb
Release : 2005-05-26
Category : Technology & Engineering
ISBN : 9780080472775
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 : Rüdiger Verfürth
Publisher : OUP Oxford
Page : 416 pages
File Size : 55,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780191668760
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,J. Tinsley Oden
Publisher : John Wiley & Sons
Page : 266 pages
File Size : 40,9 Mb
Release : 2011-09-28
Category : Mathematics
ISBN : 9781118031070
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 : Alfred Schmidt,Kunibert G. Siebert
Publisher : Springer Science & Business Media
Page : 329 pages
File Size : 49,5 Mb
Release : 2006-03-30
Category : Computers
ISBN : 9783540271567
During the last years, scientific computing has become an important research branch located between applied mathematics and applied sciences and engineering. Highly efficient numerical methods are based on adaptive methods, higher order discretizations, fast linear and non-linear iterative solvers, multi-level algorithms, etc. Such methods are integrated in the adaptive finite element software ALBERTA. It is a toolbox for the fast and flexible implementation of efficient software for real life applications, based on modern algorithms. ALBERTA also serves as an environment for improving existent, or developing new numerical methods in an interplay with mathematical analysis and it allows the direct integration of such new or improved methods in existing simulation software.
Author : Rudiger Verfurth,Rüdiger Verfürth
Publisher : Oxford University Press
Page : 414 pages
File Size : 49,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9780199679423
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 : Massimo Rudan,Rossella Brunetti,Susanna Reggiani
Publisher : Springer Nature
Page : 1680 pages
File Size : 55,8 Mb
Release : 2022-11-10
Category : Technology & Engineering
ISBN : 9783030798277
This Springer Handbook comprehensively covers the topic of semiconductor devices, embracing all aspects from theoretical background to fabrication, modeling, and applications. Nearly 100 leading scientists from industry and academia were selected to write the handbook's chapters, which were conceived for professionals and practitioners, material scientists, physicists and electrical engineers working at universities, industrial R&D, and manufacturers. Starting from the description of the relevant technological aspects and fabrication steps, the handbook proceeds with a section fully devoted to the main conventional semiconductor devices like, e.g., bipolar transistors and MOS capacitors and transistors, used in the production of the standard integrated circuits, and the corresponding physical models. In the subsequent chapters, the scaling issues of the semiconductor-device technology are addressed, followed by the description of novel concept-based semiconductor devices. The last section illustrates the numerical simulation methods ranging from the fabrication processes to the device performances. Each chapter is self-contained, and refers to related topics treated in other chapters when necessary, so that the reader interested in a specific subject can easily identify a personal reading path through the vast contents of the handbook.
Author : Ildar B. Badriev,Victor Banderov,Sergey A. Lapin
Publisher : Springer Nature
Page : 607 pages
File Size : 46,9 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 9783030878092
This book gathers papers presented at the 13th International Conference on Mesh Methods for Boundary-Value Problems and Applications, which was held in Kazan, Russia, in October 2020. The papers address the following topics: the theory of mesh methods for boundary-value problems in mathematical physics; non-linear mathematical models in mechanics and physics; algorithms for solving variational inequalities; computing science; and educational systems. Given its scope, the book is chiefly intended for students in the fields of mathematical modeling science and engineering. However, it will also benefit scientists and graduate students interested in these fields.
Author : Ivo Babuska,Joseph E. Flaherty,William D. Henshaw,John E. Hopcroft,Joseph E. Oliger,Tayfun Tezduyar
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 53,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242482
With considerations such as complex-dimensional geometries and nonlinearity, the computational solution of partial differential systems has become so involved that it is important to automate decisions that have been normally left to the individual. This book covers such decisions: 1) mesh generation with links to the software generating the domain geometry, 2) solution accuracy and reliability with mesh selection linked to solution generation. This book is suited for mathematicians, computer scientists and engineers and is intended to encourage interdisciplinary interaction between the diverse groups.
Author : Sergey I. Repin
Publisher : Walter de Gruyter
Page : 329 pages
File Size : 51,5 Mb
Release : 2008-10-31
Category : Mathematics
ISBN : 9783110203042
This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis. After giving an overview of the methods developed for models based on partial differential equations, the author derives computable a posteriori error estimates by using methods of the theory of partial differential equations and functional analysis. These estimates are applicable to approximate solutions computed by various methods.
Author : Khaled Elleithy
Publisher : Springer Science & Business Media
Page : 569 pages
File Size : 45,7 Mb
Release : 2007-08-28
Category : Technology & Engineering
ISBN : 9781402062643
This book includes a set of rigorously reviewed world-class manuscripts addressing and detailing state-of-the-art research projects in the areas of Computing Sciences, Software Engineering and Systems. The book presents selected papers from the conference proceedings of the International Conference on Systems, Computing Sciences and Software Engineering (SCSS 2006). All aspects of the conference were managed on-line.
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 : 40,7 Mb
Release : 2003-08-01
Category : Technology & Engineering
ISBN : 9780470857977
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
Author : Johannes Kraus,Ulrich Langer
Publisher : Walter de Gruyter
Page : 241 pages
File Size : 42,7 Mb
Release : 2011-12-22
Category : Mathematics
ISBN : 9783110927092
This book contains four survey papers related to different topics in computational mechanics, in particular (1) novel discretization and solver techniques in mechanics and (2) inverse, control, and optimization problems in mechanics. These topics were considered in lectures, seminars, tutorials, and workshops at the Special Semester on Computational Mechanics held at the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, in December 2005.
Author : Ivo Babuška,Theofanis Strouboulis
Publisher : Oxford University Press
Page : 820 pages
File Size : 41,6 Mb
Release : 2001
Category : Mathematics
ISBN : 0198502761
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.