Numerical Methods for Nonlinear Partial Differential Equations

✍ Scribed by Sören Bartels (auth.)

Publisher: Springer International Publishing
Year: 2015
Tongue: English
Leaves: 394
Series: Springer Series in Computational Mathematics 47
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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....Pages i-x
Introduction....Pages 1-8
Front Matter....Pages 9-9
Analytical Background....Pages 11-44
FEM for Linear Problems....Pages 45-84
Concepts for Discretized Problems....Pages 85-123
Front Matter....Pages 125-125
The Obstacle Problem....Pages 127-152
The Allen–Cahn Equation....Pages 153-182
Harmonic Maps....Pages 183-215
Bending Problems....Pages 217-257
Front Matter....Pages 259-259
Nonconvexity and Microstructure....Pages 261-295
Free Discontinuities....Pages 297-332
Elastoplasticity....Pages 333-363
Back Matter....Pages 365-393

✦ Subjects

Numerical Analysis; Partial Differential Equations; Algorithms; Calculus of Variations and Optimal Control; Optimization

📜 SIMILAR VOLUMES

Numerical Methods For Partial Differenti

📁 Numerical Methods For Partial Differential Equations

✍ William F Ames 📂 Library 📅 1984 🏛 Academic Press Inc 🌐 English

This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requirement

Numerical methods for partial differenti

📁 Numerical methods for partial differential equations

✍ William F. Ames 📂 Library 📅 1977 🏛 Elsevier 🌐 English

Numerical Methods for Partial Differenti

📁 Numerical Methods for Partial Differential Equations

✍ G. Evans, J. Blackledge, P. Yardley 📂 Library 📅 1999 🏛 Springer 🌐 English

The subject of partial differential equations holds an exciting place in mathematics. Inevitably, the subject falls into several areas of mathematics. At one extreme the interest lies in the existence and uniqueness of solutions, and the functional analysis of the proofs of these properties. At the

Numerical methods for partial differenti

📁 Numerical methods for partial differential equations

✍ Gwynne Evans; J M Blackledge; P Yardley 📂 Library 📅 2000 🏛 Springer 🌐 English

"The book presents a clear introduction of the methods and underlying theory used in the numerical solution of partial differential equations. Throughout, the emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour. After revising the mathematical p

Numerical Methods for Partial Differenti

📁 Numerical Methods for Partial Differential Equations

✍ Gwynne A. Evans MA, Dphil, DSc, Jonathan M. Blackledge BSc, PhD, DIC, Peter D. Y 📂 Library 📅 2000 🏛 Springer-Verlag London 🌐 English

<p>The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied

Numerical Methods For Partial Differenti

📁 Numerical Methods For Partial Differential Equations

✍ William F. Ames 📂 Library 📅 1977 🏛 Academic Press 🌐 English

<span>This volume is designed as an introduction to the concepts of modern numerical analysis as they apply to partial differential equations. The book contains many practical problems and their solutions, but at the same time, strives to expose the pitfalls--such as overstability, consistency requi