Numerical methods for nonlinear partial differential equations [electronic resource]

• 作者： Bartels, Soren.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Springer series in computational mathematics
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Springer series in computational mathematicsv.47
• 主題： Differential equations, Partial--Numerical solutions , Differential equations, Nonlinear , Numerical analysis , Mathematics , Numerical analysis , Partial Differential Equations. , Algorithms , Calculus of Variations and Optimal Control; Optimization.
• ISBN： 9783319137971 (electronic bk.) 、 9783319137964 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 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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• 摘要註: 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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