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010   $a3-319-13797-2
024 7 $a10.1007/978-3-319-13797-1
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100   $a20150119d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aNumerical methods for nonlinear partial differential equations /$fby Sören Bartels
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (394 p.)
225 1 $aSpringer Series in Computational Mathematics,$x0179-3632 ;$v47
300   $aDescription based upon print version of record.
311   $a3-319-13796-4 
320   $aIncludes bibliographical references at the end of each chapters and index.
327   $a1. 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.
330   $aThe description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
410  0$aSpringer Series in Computational Mathematics,$x0179-3632 ;$v47
606   $aNumerical analysis
606   $aPartial differential equations
606   $aAlgorithms
606   $aCalculus of variations
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aAlgorithms$3https://scigraph.springernature.com/ontologies/product-market-codes/M14018
606   $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016
615  0$aNumerical analysis.
615  0$aPartial differential equations.
615  0$aAlgorithms.
615  0$aCalculus of variations.
615 14$aNumerical Analysis.
615 24$aPartial Differential Equations.
615 24$aAlgorithms.
615 24$aCalculus of Variations and Optimal Control; Optimization.
676   $a510
676   $a515.353
676   $a515.64
676   $a518
676   $a518.1
700   $aBartels$b Sören$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755547
906   $aBOOK
912   $a9910299783903321
996   $aNumerical methods for nonlinear partial differential equations$91522542
997   $aUNINA