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03171nam a22005175i 4500 |
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978-3-319-13797-1 |
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DE-He213 |
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20151030061237.0 |
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cr nn 008mamaa |
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150119s2015 gw | s |||| 0|eng d |
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|a 9783319137971
|9 978-3-319-13797-1
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|a 10.1007/978-3-319-13797-1
|2 doi
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|d GrThAP
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|a QA297-299.4
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|a PBKS
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|a MAT021000
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|a MAT006000
|2 bisacsh
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|a 518
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|a Bartels, Sören.
|e author.
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|a Numerical Methods for Nonlinear Partial Differential Equations
|h [electronic resource] /
|c by Sören Bartels.
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|a Cham :
|b Springer International Publishing :
|b Imprint: Springer,
|c 2015.
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|a X, 393 p. 122 illus.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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|a Springer Series in Computational Mathematics,
|x 0179-3632 ;
|v 47
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|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.
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|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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| 650 |
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|a Mathematics.
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| 650 |
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|a Partial differential equations.
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| 650 |
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|a Algorithms.
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| 650 |
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|a Numerical analysis.
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| 650 |
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|a Calculus of variations.
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| 650 |
1 |
4 |
|a Mathematics.
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| 650 |
2 |
4 |
|a Numerical Analysis.
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| 650 |
2 |
4 |
|a Partial Differential Equations.
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| 650 |
2 |
4 |
|a Algorithms.
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| 650 |
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|a Calculus of Variations and Optimal Control; Optimization.
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| 710 |
2 |
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783319137964
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| 830 |
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|a Springer Series in Computational Mathematics,
|x 0179-3632 ;
|v 47
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| 856 |
4 |
0 |
|u http://dx.doi.org/10.1007/978-3-319-13797-1
|z Full Text via HEAL-Link
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| 912 |
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|a ZDB-2-SMA
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| 950 |
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|a Mathematics and Statistics (Springer-11649)
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