04085nam 22007215 450 991029978390332120220415175413.03-319-13797-210.1007/978-3-319-13797-1(CKB)3710000000342469(EBL)1963402(SSID)ssj0001424549(PQKBManifestationID)11809156(PQKBTitleCode)TC0001424549(PQKBWorkID)11367518(PQKB)10641445(DE-He213)978-3-319-13797-1(MiAaPQ)EBC1963402(PPN)183520572(EXLCZ)99371000000034246920150119d2015 u| 0engur|n|---|||||txtccrNumerical methods for nonlinear partial differential equations[electronic resource] /by Sören Bartels1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (394 p.)Springer Series in Computational Mathematics,0179-3632 ;47Description based upon print version of record.3-319-13796-4 Includes bibliographical references at the end of each chapters and index.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.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.Springer Series in Computational Mathematics,0179-3632 ;47Numerical analysisPartial differential equationsAlgorithmsCalculus of variationsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Algorithmshttps://scigraph.springernature.com/ontologies/product-market-codes/M14018Calculus of Variations and Optimal Control; Optimizationhttps://scigraph.springernature.com/ontologies/product-market-codes/M26016Numerical analysis.Partial differential equations.Algorithms.Calculus of variations.Numerical Analysis.Partial Differential Equations.Algorithms.Calculus of Variations and Optimal Control; Optimization.510515.353515.64518518.1Bartels Sörenauthttp://id.loc.gov/vocabulary/relators/aut755547BOOK9910299783903321Numerical methods for nonlinear partial differential equations1522542UNINA