A Posteriori Error Estimation in Finite Element Analysis / Edition 1

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Overview

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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Editorial Reviews

Booknews
For applied mathematicians and engineers who have an interest in either error estimation or finite elements, Ainsworth (applied mathematics, Strathclyde U.) and Oden (computational and applied mathematics, U. of Texas-Austin) introduces methods for estimating the inevitable discretization error produced by numerical procedures. They explain the mathematical underpinnings of the methods and their implementation on boundary value problems of continuum mechanics and physics. They focus mostly on model scalar elliptic problems on two- dimensional domains to keep the discussion uncluttered, but do present significant generalizations to unsymmetric, indefinite problems and to representative nonlinear problems such as the Navier-Stokes equation. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

Meet the Author

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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Table of Contents

Explicit A Posteriori Estimators.

Implicit A Posteriori Estimators.

Recovery Based Error Estimators.

Estimators, Indicators, and Hierarchic Bases.

The Equilibrated Residual Method.

Methodology for the Comparison of Estimators.

Estimation of the Errors in Quantities of Interest.

Some Extensions.

References.

Index.

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