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Numerical methods for nonlinear partial differential equations / / by Sören Bartels



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Autore: Bartels Sören Visualizza persona
Titolo: Numerical methods for nonlinear partial differential equations / / by Sören Bartels Visualizza cluster
Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
Edizione: 1st ed. 2015.
Descrizione fisica: 1 online resource (394 p.)
Disciplina: 510
515.353
515.64
518
518.1
Soggetto topico: Numerical analysis
Partial differential equations
Algorithms
Calculus of variations
Numerical Analysis
Partial Differential Equations
Calculus of Variations and Optimal Control; Optimization
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
Nota di contenuto: 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.
Sommario/riassunto: 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.
Titolo autorizzato: Numerical methods for nonlinear partial differential equations  Visualizza cluster
ISBN: 3-319-13797-2
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910299783903321
Lo trovi qui: Univ. Federico II
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Serie: Springer Series in Computational Mathematics, . 0179-3632 ; ; 47