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A Posteriori Error Analysis via Duality TheoryError Analysis for Variational Inequalities of the Second Kind

A Posteriori Error Analysis via Duality Theory: Error Analysis for Variational Inequalities of... Chapter 6 ERROR ANALYSIS FOR VARIATIONAL INEQUALITIES OF THE SECOND KIND The finite element method today is the dominant numerical method for solv- ing most problems in structural and fluid mechanics. It is widely applied to both linear and nonlinear problems. For practical use of the method, one of the most important problems is the assessment of the reliability of a finite element solu- tion. The reliability of the numerical solution hinges on our ability to estimate errors after the solution is computed; such an error analysis is called a posteriori error analysis. A posteriori error estimates provide quantitative information on the accuracy of the solution and are the basis for the development of automatic, adaptive procedures for engineering applications of the finite element method. The research on a posteriori error estimation and adaptive mesh refinement for the finite element method began in the late 1970's. The pioneering work on the topic was done in [l 1, 121. Since then, a posteriori error analysis and adap- tive computation in the finite element method have attracted many researchers, and a variety of different a posteriori error estimates have been proposed and analyzed. In a typical a posteriori error analysis, after http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Posteriori Error Analysis via Duality TheoryError Analysis for Variational Inequalities of the Second Kind

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Publisher
Springer US
Copyright
© Springer Science+Business Media, Inc. 2005
ISBN
978-0-387-23536-3
Pages
235 –285
DOI
10.1007/0-387-23537-X_6
Publisher site
See Chapter on Publisher Site

Abstract

Chapter 6 ERROR ANALYSIS FOR VARIATIONAL INEQUALITIES OF THE SECOND KIND The finite element method today is the dominant numerical method for solv- ing most problems in structural and fluid mechanics. It is widely applied to both linear and nonlinear problems. For practical use of the method, one of the most important problems is the assessment of the reliability of a finite element solu- tion. The reliability of the numerical solution hinges on our ability to estimate errors after the solution is computed; such an error analysis is called a posteriori error analysis. A posteriori error estimates provide quantitative information on the accuracy of the solution and are the basis for the development of automatic, adaptive procedures for engineering applications of the finite element method. The research on a posteriori error estimation and adaptive mesh refinement for the finite element method began in the late 1970's. The pioneering work on the topic was done in [l 1, 121. Since then, a posteriori error analysis and adap- tive computation in the finite element method have attracted many researchers, and a variety of different a posteriori error estimates have been proposed and analyzed. In a typical a posteriori error analysis, after

Published: Jan 1, 2005

Keywords: Variational Inequality; Error Estimator; Duality Theory; Posteriori Error; Posteriori Error Estimate

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