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Numerical methods for nonlinear part...

Bartels, Soren.

Numerical methods for nonlinear partial differential equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical methods for nonlinear partial differential equationsby Soren Bartels.
Author:	Bartels, Soren.
Published:	Cham :Springer International Publishing :2015.
Description:	x, 393 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Numerical Analysis.
Online resource:	http://dx.doi.org/10.1007/978-3-319-13797-1
ISBN:	9783319137971 (electronic bk.)

Numerical methods for nonlinear partial differential equations
Bartels, Soren.

Numerical methods for nonlinear partial differential equations[electronic resource] /by Soren Bartels. - Cham :Springer International Publishing :2015. - x, 393 p. :ill., digital ;24 cm. - Springer series in computational mathematics,v.470179-3632 ;. - Springer series in computational mathematics ;42..

1. Introduction -- Part I: Analytical and Numerical Foundations -- 2. Analytical Background -- 3. FEM for Linear Problems -- 4. Concepts for Discretized Problems -- Part II: Approximation of Classical Formulations -- 5. The Obstacle Problem -- 6. The Allen-Cahn Equation -- 7. Harmonic Maps -- 8. Bending Problems -- Part III: Methods for Extended Formulations -- 9. Nonconvexity and Microstructure -- 10. Free Discontinuities -- 11. Elastoplasticity -- Auxiliary Routines -- Frequently Used Notation -- Index.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

ISBN: 9783319137971 (electronic bk.)

Standard No.: 10.1007/978-3-319-13797-1doiSubjects--Topical Terms:

275681
Numerical Analysis.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Numerical methods for nonlinear partial differential equations
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245 1 0 $a Numerical methods for nonlinear partial differential equations $h [electronic resource] / $c by Soren Bartels.
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505 0 $a 1. Introduction -- Part I: Analytical and Numerical Foundations -- 2. Analytical Background -- 3. FEM for Linear Problems -- 4. Concepts for Discretized Problems -- Part II: Approximation of Classical Formulations -- 5. The Obstacle Problem -- 6. The Allen-Cahn Equation -- 7. Harmonic Maps -- 8. Bending Problems -- Part III: Methods for Extended Formulations -- 9. Nonconvexity and Microstructure -- 10. Free Discontinuities -- 11. Elastoplasticity -- Auxiliary Routines -- Frequently Used Notation -- Index.
520 $a The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
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