A Posteriori Estimates For Partial Differential Equations
DOWNLOAD
Download A Posteriori Estimates For Partial Differential Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Posteriori Estimates For Partial Differential Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
A Posteriori Estimates For Partial Differential Equations
DOWNLOAD
Author : Sergey I. Repin
language : en
Publisher: Walter de Gruyter
Release Date : 2008-10-31
A Posteriori Estimates For Partial Differential Equations written by Sergey I. Repin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-31 with Mathematics categories.
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.
A Posteriori Error Estimation Techniques For Finite Element Methods
DOWNLOAD
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.
Some A Posteriori Error Estimates For Elliptic Partial Differential Equations
DOWNLOAD
Author : M. R. Phillips
language : en
Publisher:
Release Date : 1997
Some A Posteriori Error Estimates For Elliptic Partial Differential Equations written by M. R. Phillips and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.
A Posteriori Error Estimation For Partial Differential Equations With Random Input Data
DOWNLOAD
Author : Diane Sylvie Guignard
language : en
Publisher:
Release Date : 2016
A Posteriori Error Estimation For Partial Differential Equations With Random Input Data written by Diane Sylvie Guignard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with categories.
Mots-clés de l'autrice: PDEs with random inputs ; uncertainty quantification ; a priori and a posteriori error analysis ; finite elements ; perturbation techniques ; stochastic collocation ; elliptic equations ; steady Navier-Stokes equations ; heat equation.
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations
DOWNLOAD
Author : Mitsuhiro T. Nakao
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations written by Mitsuhiro T. Nakao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
Residual Type A Posteriori Error Estimates For Semi Linear Parabolic Partial Differential Equations
DOWNLOAD
Author :
language : en
Publisher:
Release Date : 2010
Residual Type A Posteriori Error Estimates For Semi Linear Parabolic Partial Differential Equations written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Differential equations categories.
A posteriori error analysis is the key idea for adaptive finite element methods for solving partial differential equations(PDEs). In this thesis, we are interested in a posteriori error analysis for semi-linear parabolic PDEs over polygonal domain in 2-D with Dirichlet boundary condition. We showed the efficiency and reliability of a posteriori error estimator by deriving the upper and local lower bounds based on the standard residual estimator under the assumption that the nonlinear function f is Lipschitz with respect to the variable u. We also constructed an algorithm for adaptive finite element method based on a posterior error estimations.
A Posteriori Estimates Of Inverse Operators For Boundary Value Problems In Linear Elliptic Partial Differential Equations
DOWNLOAD
Author : Yoshitaka Watanabe
language : en
Publisher:
Release Date : 2011
A Posteriori Estimates Of Inverse Operators For Boundary Value Problems In Linear Elliptic Partial Differential Equations written by Yoshitaka Watanabe and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Differential equations, Elliptic categories.
Smil 3 0
DOWNLOAD
Author : Dick C.A. Bulterman
language : en
Publisher: Springer
Release Date : 2008-11-20
Smil 3 0 written by Dick C.A. Bulterman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-20 with Computers categories.
SMIL 3.0: Multimedia for the Web, Mobile Devices and Daisy Talking Books is a revised introduction to — and resource guide for — the W3C SMIL language. It covers all aspects of the SMIL specification and covers all of SMIL’s implem- tation profiles, from the desktop through the world of mobile SMIL devices. Based on the first version of the book, which covered SMIL 2.0, this edition has been updated with information from the past two releases of the SMIL l- guage. We have benefitted from comments and suggestions from many readers of the first edition, and have produced what we feel is the most comprehensive guide to SMIL available anywhere. Motivation for this Book While we were working on various phases of the SMIL recommendations, it became clear to us that the richness of the SMIL language could easily ov- whelm many Web authors and designers. In the 500+ pages that the SYMM working group needed to describe the 30+ SMIL elements and the 150+ SMIL attributes, there was not much room for background information or extensive examples. The focus of the specification was on implementation aspects of the SMIL language, not on the rationale or the potential uses of SMIL’s declarative power.
Partial Differential Equations
DOWNLOAD
Author : D. Sloan
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Partial Differential Equations written by D. Sloan and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Mathematics categories.
/homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight into the underlying stability and accuracy properties of computational algorithms for PDEs was deepened by building upon recent progress in mathematical analysis and in the theory of PDEs. To embark on a comprehensive review of the field of numerical analysis of partial differential equations within a single volume of this journal would have been an impossible task. Indeed, the 16 contributions included here, by some of the foremost world authorities in the subject, represent only a small sample of the major developments. We hope that these articles will, nevertheless, provide the reader with a stimulating glimpse into this diverse, exciting and important field. The opening paper by Thomée reviews the history of numerical analysis of PDEs, starting with the 1928 paper by Courant, Friedrichs and Lewy on the solution of problems of mathematical physics by means of finite differences. This excellent survey takes the reader through the development of finite differences for elliptic problems from the 1930s, and the intense study of finite differences for general initial value problems during the 1950s and 1960s. The formulation of the concept of stability is explored in the Lax equivalence theorem and the Kreiss matrix lemmas. Reference is made to the introduction of the finite element method by structural engineers, and a description is given of the subsequent development and mathematical analysis of the finite element method with piecewise polynomial approximating functions. The penultimate section of Thomée's survey deals with `other classes of approximation methods', and this covers methods such as collocation methods, spectral methods, finite volume methods and boundary integral methods. The final section is devoted to numerical linear algebra for elliptic problems. The next three papers, by Bialecki and Fairweather, Hesthaven and Gottlieb and Dahmen, describe, respectively, spline collocation methods, spectral methods and wavelet methods. The work by Bialecki and Fairweather is a comprehensive overview of orthogonal spline collocation from its first appearance to the latest mathematical developments and applications. The emphasis throughout is on problems in two space dimensions. The paper by Hesthaven and Gottlieb presents a review of Fourier and Chebyshev pseudospectral methods for the solution of hyperbolic PDEs. Particular emphasis is placed on the treatment of boundaries, stability of time discretisations, treatment of non-smooth solutions and multidomain techniques. The paper gives a clear view of the advances that have been made over the last decade in solving hyperbolic problems by means of spectral methods, but it shows that many critical issues remain open. The paper by Dahmen reviews the recent rapid growth in the use of wavelet methods for PDEs. The author focuses on the use of adaptivity, where significant successes have recently been achieved. He describes the potential weaknesses of wavelet methods as well as the perceived strengths, thus giving a balanced view that should encourage the study of wavelet methods.
A Posteriori Error Estimates For Semi Linear Elliptic Partial Differential Equations
DOWNLOAD
Author : Suttisak Jampawai
language : en
Publisher:
Release Date : 2009
A Posteriori Error Estimates For Semi Linear Elliptic Partial Differential Equations written by Suttisak Jampawai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Differential equations categories.
We derive upper and lower bounds for a posteriori error estimates in finite element solutions of semi-linear elliptic partial differential equations (PDEs) over polygonal domains in two space dimensions. We consider the Dirichlet problem for semi-linear PDEs with vanishing boundary. The estimate is based on Lagrange element, and the error estimates are computed in the energy norm with assumption of exact integration. The proof is based on the condition of function f(x, u) which have first derivative in second argument.