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Bartels S. Numerical Methods for Nonlinear Partial Differential Equations

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Bartels S. Numerical Methods for Nonlinear Partial Differential Equations
N.-Y.: Springer, 2015. - 396p.
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.
Table of contents :
Front Matter.
Analytical Background.
FEM for Linear Problems.
Concepts for Discretized Problems.
Front Matter.
The Obstacle Problem.
The Allen–Cahn Equation.
Harmonic Maps.
Bending Problems.
Front Matter.
Nonconvexity and Microstructure.
Free Discontinuities.
Back Matter.
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