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A Posteriori Error Analysis via Duality TheoryA Posteriori Error Analysis for Linearizations

A Posteriori Error Analysis via Duality Theory: A Posteriori Error Analysis for Linearizations Chapter 4 A POSTERIORI ERROR ANALYSIS FOR LINEARIZATIONS Linearization technique is used frequently in modeling physical phenomena and in numerical computations. In this chapter, we derive a posteriori error esti- mates for the effect of linearization on solutions of nonlinear physical problems. A posteriori error estimates for the linearization technique used in numerical approximations will be derived in the Chapter 5. 4.1. LINEARIZATION OF A NONLINEAR BOUNDARY VALUE PROBLEM Detailed quantitative error analysis is given for linearizations of certain non- linear elliptic problems, whose linearizations are boundary value problems of Poisson's equations. An example of a nonlinear problem considered in this section is the following: When R c IK2 is a planar Lipschitz domain, for suitable data a, f and g, the problem (4.1)-(4.2) describes a nonlinear torsion problem (cf. [109]). In particular, when the coefficient function a(() = 1, the problem (4.1)-(4.2) reduces to which represents a linear torsion problem (cf. Section 3.5). Owing to the diffi- culty associated with determining the material property function a((), in most elasticity theory books, it is taken for granted that the torsion problem of a A POSTERIORI ERROR ANALYSIS VIA DUALITY THEORY real material has been described accurately enough by the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Posteriori Error Analysis via Duality TheoryA Posteriori Error Analysis for Linearizations

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Publisher
Springer US
Copyright
© Springer Science+Business Media, Inc. 2005
ISBN
978-0-387-23536-3
Pages
127 –192
DOI
10.1007/0-387-23537-X_4
Publisher site
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Abstract

Chapter 4 A POSTERIORI ERROR ANALYSIS FOR LINEARIZATIONS Linearization technique is used frequently in modeling physical phenomena and in numerical computations. In this chapter, we derive a posteriori error esti- mates for the effect of linearization on solutions of nonlinear physical problems. A posteriori error estimates for the linearization technique used in numerical approximations will be derived in the Chapter 5. 4.1. LINEARIZATION OF A NONLINEAR BOUNDARY VALUE PROBLEM Detailed quantitative error analysis is given for linearizations of certain non- linear elliptic problems, whose linearizations are boundary value problems of Poisson's equations. An example of a nonlinear problem considered in this section is the following: When R c IK2 is a planar Lipschitz domain, for suitable data a, f and g, the problem (4.1)-(4.2) describes a nonlinear torsion problem (cf. [109]). In particular, when the coefficient function a(() = 1, the problem (4.1)-(4.2) reduces to which represents a linear torsion problem (cf. Section 3.5). Owing to the diffi- culty associated with determining the material property function a((), in most elasticity theory books, it is taken for granted that the torsion problem of a A POSTERIORI ERROR ANALYSIS VIA DUALITY THEORY real material has been described accurately enough by the

Published: Jan 1, 2005

Keywords: Error Bound; Duality Theory; Posteriori Error; Lipschitz Domain; Obstacle Problem

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