On Superconvergence Up to Boundaries in Finite Element Methods
Author : Lars B. Wahlbin
Publisher :
Page : 32 pages
File Size : 34,88 MB
Release : 1991
Category :
ISBN :
Superconvergence in Galerkin Finite Element Methods
Author : Lars Wahlbin
Publisher : Springer
Page : 179 pages
File Size : 22,14 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540494014
Book Description
This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.
Finite Element Methods
Author : Michel Krizek
Publisher : Routledge
Page : 370 pages
File Size : 23,62 MB
Release : 2017-11-22
Category : Mathematics
ISBN : 1351448609
Book Description
""Based on the proceedings of the first conference on superconvergence held recently at the University of Jyvaskyla, Finland. Presents reviewed papers focusing on superconvergence phenomena in the finite element method. Surveys for the first time all known superconvergence techniques, including their proofs.
Recent Advances in Computational Sciences
Author : Palle E. T. J0rgensen
Publisher : World Scientific
Page : 395 pages
File Size : 11,31 MB
Release : 2008
Category : Mathematics
ISBN : 9812792384
Book Description
This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrodinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book. This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.
Recent Advances In Computational Sciences: Selected Papers From The International Workshop On Computational Sciences And Its Education
Author : Xiaoping Shen
Publisher : World Scientific
Page : 395 pages
File Size : 20,87 MB
Release : 2008-07-31
Category : Mathematics
ISBN : 981447536X
Book Description
This book presents state-of-the-art lectures delivered by international academic and industrial experts in the field of computational science and its education, covering a wide spectrum from theory to practice. Topics include new developments in finite element method (FEM), finite volume method and Spline theory, such as Moving Mesh Methods, Galerkin and Discontinuous Galerkin Schemes, Shape Gradient Methods, Mixed FEMs, Superconvergence techniques and Fourier spectral approximations with applications in multidimensional fluid dynamics; Maxwell equations in discrepancy media; and phase-field equations. It also discusses some interesting topics related to Stokes equations, Schrödinger equations, wavelet analysis and approximation theory. Contemporary teaching issues in curriculum reform also form an integral part of the book.This book will therefore be of significant interest and value to all graduates, research scientists and practitioners facing complex computational problems. Administrators and policymakers will find it is an addition to their mathematics curriculum reform libraries.
Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations
Author : Xiaobing Feng
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 17,69 MB
Release : 2013-11-08
Category : Mathematics
ISBN : 3319018183
Book Description
The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
Fitted Numerical Methods For Singular Perturbation Problems: Error Estimates In The Maximum Norm For Linear Problems In One And Two Dimensions (Revised Edition)
Author : John J H Miller
Publisher : World Scientific
Page : 191 pages
File Size : 19,33 MB
Release : 2012-02-29
Category : Mathematics
ISBN : 9814452777
Book Description
Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly. Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh methods.
Computer Mathematics
Author : Xiao-Shan Gao
Publisher : World Scientific
Page : 338 pages
File Size : 16,5 MB
Release : 2000
Category : Computers
ISBN : 9810244983
Book Description
This volume contains selected papers presented at the Fourth Asian Symposium on Computer Mathematics. 39 peer-reviewed original contributions together with full papers and extended abstracts by the four invited speakers, G H Gonnet, D Lazard, W McCune, and W-T Wu, cover some of the most recent and significant advances in computer mathematics, including algebraic, symbolic, numeric, and geometric computation, automated mathematical reasoning, mathematical software, and computer-aided geometric design. Researchers, teachers, students, and engineers interested in doing mathematics using computers will find this volume good reading and a valuable reference.
Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations
Author : Ivo Babuska
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 18,63 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461242487
Book Description
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.
The Finite Element Method and Its Reliability
Author : Ivo Babuška
Publisher : Oxford University Press
Page : 820 pages
File Size : 49,36 MB
Release : 2001
Category : Mathematics
ISBN : 9780198502760
Book Description
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.
