A Posteriori Error Estimation in Finite Element Analysis

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John Wiley & Sons, Sep 4, 2000 - Mathematics - 240 pages
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An up-to-date, one-stop reference–complete with applications

This volume presents the most up-to-date information available on a posteriori error estimation for finite element approximation in mechanics and mathematics. It emphasizes methods for elliptic boundary value problems and includes applications to incompressible flow and nonlinear problems.

Recent years have seen an explosion in the study of a posteriori error estimators due to their remarkable influence on improving both accuracy and reliability in scientific computing. In an effort to provide an accessible source, the authors have sought to present key ideas and common principles on a sound mathematical footing.

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 lucid and convenient resource for researchers in almost any field of finite element methods, and for applied mathematicians and engineers who have an interest in error estimation and/or finite elements.

  

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Contents

Introduction
1
Explicit A Posteriori Estimators
19
Implicit A Posteriori Estimators
43
RecoveryBased Error Estimators
65
Estimators Indicators and Hierarchic Bases
85
The Equilibrated Residual Method
111
Methodolo9y for the Comparison of Estimators
145
Estimation of the Errors in Quantities of Interest
189
Some Extensions
207
References
229
Index
239
Copyright

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About the author (2000)

MARK AINSWORTH, PhD, is Professor of Applied Mathematics at Strathclyde University, UK.
J. TINSLEY ODEN, PhD, is Director of the Texas Institute for Computational and Applied Mathematics at the University of Texas, Austin.

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