A Posteriori Error Estimates For Semi Linear Elliptic Partial Differential Equations
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A Posteriori Error Estimates For Semi Linear Elliptic Partial Differential Equations
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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.
Residual Type A Posteriori Error Estimates For Semi Linear Parabolic Partial Differential Equations
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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.
Some A Posteriori Error Estimates For Elliptic Partial Differential Equations
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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 Estimates For Partial Differential Equations
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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.
Partial Differential Equations
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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 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 Posteriori Error Estimation For Partial Differential Equations With Random Input Data
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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.
Pointwise A Posteriori Error Estimates For Monotone Semi Linear Equations
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Author :
language : en
Publisher:
Release Date : 2005
Pointwise A Posteriori Error Estimates For Monotone Semi Linear 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 2005 with categories.
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 For Hybridized Mixed And Discontinuous Galerkin Methods
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Author : Johannes Neher
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2012
A Posteriori Error Estimation For Hybridized Mixed And Discontinuous Galerkin Methods written by Johannes Neher and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
There is a variety of finite element based methods applicable to the discretization of second order elliptic boundary value problems in mixed form. However, it is expensive to solve the resulting discrete linear system due to its size and its algebraic structure. Hybridization serves as a tool to circumvent these difficulties. Furthermore hybridization is an elegant concept to establish connections among various finite element methods. In this work connections between the methods and their hybridized counterparts are established after showing the link between three different formulations of the elliptic model problem. The main part of the work contains the development of a reliable a posteriori error estimator, which is applicable to all of the methods above. This estimator is the key ingredient of an adaptive numerical approximation of the original boundary value problem. Finally, a number of numerical tests is discussed in order to exhibit the performance of the adaptive hybridized methods.