An Adaptive Finite Element Method With Efficient Maximum Norm Error Control For Elliptic Problems
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An Adaptive Finite Element Method With Efficient Maximum Norm Error Control For Elliptic Problems
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Author : Kenneth Eriksson
language : en
Publisher:
Release Date : 1993
An Adaptive Finite Element Method With Efficient Maximum Norm Error Control For Elliptic Problems written by Kenneth Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
An Adaptive Finite Element Method With Efficient Maximum Norm Error Controlfor Elliptic Problems
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Author : K. Eriksson
language : en
Publisher:
Release Date : 1993
An Adaptive Finite Element Method With Efficient Maximum Norm Error Controlfor Elliptic Problems written by K. Eriksson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Adaptive Finite Element Methods For Differential Equations
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Author : Wolfgang Bangerth
language : en
Publisher: Birkhäuser
Release Date : 2013-11-11
Adaptive Finite Element Methods For Differential Equations written by Wolfgang Bangerth and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.
Recent Advances In Adaptive Computation
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Author : Zhongci Shi
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Recent Advances In Adaptive Computation written by Zhongci Shi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Computers categories.
There has been rapid development in the area of adaptive computation over the past decade. The International Conference on Recent Advances in Adaptive Computation was held at Zhejiang University (Hangzhou, China) to explore these new directions. The conference brought together specialists to discuss modern theories and practical applications of adaptive methods. This volume contains articles reflecting the invited talks given by leading mathematicians at the conference. It is suitable for graduate students and researchers interested in methods of computation.
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations
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Author : Donald J. Estep
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Estimating The Error Of Numerical Solutions Of Systems Of Reaction Diffusion Equations written by Donald J. Estep and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This paper is concerned with the computational estimation of the error of numerical solutions of potentially degenerate reaction-diffusion equations. The underlying motivation is a desire to compute accurate estimates as opposed to deriving inaccurate analytic upper bounds. In this paper, we outline, analyze, and test an approach to obtain computational error estimates based on the introduction of the residual error of the numerical solution and in which the effects of the accumulation of errors are estimated computationally. We begin by deriving an a posteriori relationship between the error of a numerical solution and its residual error using a variational argument. This leads to the introduction of stability factors, which measure the sensitivity of solutions to various kinds of perturbations. Next, we perform some general analysis on the residual errors and stability factors to determine when they are defined and to bound their size. Then we describe the practical use of the theory to estimate the errors of numerical solutions computationally. Several key issues arise in the implementation that remain unresolved and we present partial results and numerical experiments about these points. We use this approach to estimate the error of numerical solutions of nine standard reaction-diffusion models and make a systematic comparison of the time scale over which accurate numerical solutions can be computed for these problems. We also perform a numerical test of the accuracy and reliability of the computational error estimate using the bistable equation. Finally, we apply the general theory to the class of problems that admit invariant regions for the solutions, which includes seven of the main examples. Under this additional stability assumption, we obtain a convergence result in the form of an upper bound on the error from the a posteriori error estimate. We conclude by discussing the preservation of invariant regions under discretization.
Acta Numerica 1995 Volume 4
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Author : Arieh Iserles
language : en
Publisher: Cambridge University Press
Release Date : 1995-07-13
Acta Numerica 1995 Volume 4 written by Arieh Iserles and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-07-13 with Mathematics categories.
Acta Numerica has established itself as the prime forum for the presentation of definitive reviews of numerical analysis topics. The invited review papers, by leaders in their respective fields, allow researchers and graduate students alike quickly to grasp trends and developments. Highlights of the 1995 issue include articles on sequential quadratic programming, mesh adaption, free boundary problems and particle methods in continuum computations.
Large Scale Scientific Computing
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Author : Ivan Lirkov
language : en
Publisher: Springer
Release Date : 2010-05-10
Large Scale Scientific Computing written by Ivan Lirkov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-10 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Large-Scale Scientific Computations, LSSC 2009, held in Sozopol, Bulgaria, in June 2009. The 93 revised full papers presented together with 5 plenary and invited papers were carefully reviewed and selected from numerous submissions for inclusion in the book. The papers are organized in topical sections on multilevel and multiscale preconditioning methods multilevel and multiscale methods for industrial applications, environmental modeling, control and uncertain systems, application of metaheuristics to large scale problems, monte carlo: methods, applications, distributed computing, grid and scientific and engineering applications, reliable numerical methods for differential equations, novel applications of optimization ideas to the numerical Solution of PDEs, and contributed talks.
Unified Multilevel Adaptive Finite Element Methods For Elliptic Problems
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Author : William F. Mitchell
language : en
Publisher:
Release Date : 1988
Unified Multilevel Adaptive Finite Element Methods For Elliptic Problems written by William F. Mitchell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Differential equations, Elliptic categories.
Adaptive Methods For Partial Differential Equations
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Author : Ivo Babushka
language : en
Publisher: SIAM
Release Date : 1989-01-01
Adaptive Methods For Partial Differential Equations written by Ivo Babushka and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-01-01 with Mathematics categories.
"Proceedings of the Workshop on Adaptive Computational Methods for Partial Differential Equations, Rensselaer Polytechnic Institute, October 13-15, 1988"--T.p. verso.
The Mathematics Of Finite Elements And Applications
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Author : J. R. Whiteman
language : en
Publisher:
Release Date : 1994
The Mathematics Of Finite Elements And Applications written by J. R. Whiteman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
World leaders in diverse disciplines, whose common interest is finite element methods, address the latest developments in the field. Mathematical theory, engineering and scientific applications, computational techniques, large scale analysis and implementation of related methods are among the subjects discussed.