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＜電子ブック＞
Numerical Methods for Nonlinear Partial Differential Equations / by Sören Bartels
(Springer Series in Computational Mathematics. ISSN:21983712 ; 47)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
本文言語	英語
大きさ	X, 393 p. 122 illus : online resource
著者標目	*Bartels, Sören author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Differential equations LCSH:Algorithms LCSH:Mathematical optimization LCSH:Calculus of variations FREE:Numerical Analysis FREE:Differential Equations FREE:Algorithms FREE:Calculus of Variations and Optimization
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-319-13797-1

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