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Field name	Details
Dewey Class	518
Title	Numerical Methods for Nonlinear Partial Differential Equations ([EBook]) / by Sören Bartels.
Author	Bartels, Sören
Other name(s)	SpringerLink (Online service)
Publication	Cham : : Springer International Publishing : : Imprint: Springer, , 2015.
Physical Details	X, 393 p. 122 illus. : online resource.
Series	Springer Series in Computational Mathematics 0179-3632 ; ; 47
ISBN	9783319137971
Summary Note	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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-13797-1
Links to Related Works	Subject References: Algorithms . Calculus of variations . Calculus of variations and optimal control; optimization . Mathematics . Numerical Analysis . Partial differential equations . Authors: Bartels, Sören . Corporate Authors: SpringerLink (Online service) . Series: Springer Series in Computational Mathematics . Classification: 518 .

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Numerical Methods for Nonlinear Partial Differential Equations

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