# A Posteriori Error Analysis via Duality TheoryA Posteriori Error Analysis for Some Numerical Procedures

A Posteriori Error Analysis via Duality Theory: A Posteriori Error Analysis for Some Numerical... Chapter 5 A POSTERIORI ERROR ANALYSIS FOR SOME NUMERICAL PROCEDURES In this chapter, we apply the duality technique to derive a posteriori error estimates for some numerical procedures, including the regularization method and the KaEanov iteration method, in solving nonlinear boundary value prob- lems. The regularization method is usually employed in numerical treatment of problems involving non-smooth terms. One family of such problems is the vari- ational inequalities of the second kind. The KaEanov iteration method provides a sequence of linear problems to approximate a nonlinear problem, and can be quite efficient when the nonlinearity is not strong. For practical implementation of the regularization method or the KaEanov method, it is highly desirable to have some a posteriori error estimate so that once a regularization iterate or KaEanov iterate is computed, we can compute a (presumably efficient) error bound for the approximate solution with ease. Such an error estimate can pro- vide us some information about the reliability of numerical solutions, and can also be used as a convenient stopping criterion for iterations. Our presentation of the a posteriori error analysis here is focused on the continuous problems, and can be easily adapted to treat the discretized problems, as http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# A Posteriori Error Analysis via Duality TheoryA Posteriori Error Analysis for Some Numerical Procedures

40 pages

/lp/springer-journals/a-posteriori-error-analysis-via-duality-theory-a-posteriori-error-VAL7ECEnEI
Publisher
Springer US
ISBN
978-0-387-23536-3
Pages
193 –233
DOI
10.1007/0-387-23537-X_5
Publisher site
See Chapter on Publisher Site

### Abstract

Chapter 5 A POSTERIORI ERROR ANALYSIS FOR SOME NUMERICAL PROCEDURES In this chapter, we apply the duality technique to derive a posteriori error estimates for some numerical procedures, including the regularization method and the KaEanov iteration method, in solving nonlinear boundary value prob- lems. The regularization method is usually employed in numerical treatment of problems involving non-smooth terms. One family of such problems is the vari- ational inequalities of the second kind. The KaEanov iteration method provides a sequence of linear problems to approximate a nonlinear problem, and can be quite efficient when the nonlinearity is not strong. For practical implementation of the regularization method or the KaEanov method, it is highly desirable to have some a posteriori error estimate so that once a regularization iterate or KaEanov iterate is computed, we can compute a (presumably efficient) error bound for the approximate solution with ease. Such an error estimate can pro- vide us some information about the reliability of numerical solutions, and can also be used as a convenient stopping criterion for iterations. Our presentation of the a posteriori error analysis here is focused on the continuous problems, and can be easily adapted to treat the discretized problems, as

Published: Jan 1, 2005

Keywords: Variational Inequality; Numerical Procedure; Duality Theory; Posteriori Error; Regularization Method