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Numerical Methods for Nonlinear Partial Differential Equations

E-BookPDF1 - PDF WatermarkE-Book
393 Seiten
Englisch
Springer International Publishingerschienen am19.01.20152015
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.mehr
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Produkt

KlappentextThe 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.
Details
Weitere ISBN/GTIN9783319137971
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2015
Erscheinungsdatum19.01.2015
Auflage2015
ReiheSpringer Series in Computational Mathematics
Reihen-Nr.47
Seiten393 Seiten
SpracheEnglisch
IllustrationenX, 393 p. 122 illus.
Artikel-Nr.1571134
Rubriken
Genre9200

Inhalt/Kritik

Inhaltsverzeichnis
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.mehr