Numerical Methods for Nonlinear Partial Differential Equations

• Main Author: Bartels, Sören (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Springer Series in Computational Mathematics, 47
• Subjects: Mathematics.; Partial differential equations.; Algorithms.; Numerical analysis.; Calculus of variations.; Numerical Analysis.; Partial Differential Equations.; Calculus of Variations and Optimal Control; Optimization.

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...

Table of Contents:

• 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.