Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems

✍ Scribed by Hans-Görg Roos, Martin Stynes, Lutz Tobiska (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2008
• Tongue: English
• Leaves: 598
• Series: Springer Series in Computational Mathematics 24
• Edition: 2
• Category: Library

✦ Synopsis

This considerably extended and completely revised second edition incorporates many new developments in the thriving field of numerical methods for singularly perturbed differential equations. It provides a thorough foundation for the numerical analysis and solution of these problems, which model many physical phenomena whose solutions exhibit layers. The book focuses on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics. It offers a comprehensive overview of suitable numerical methods while emphasizing those with realistic error estimates. The book should be useful for scientists requiring effective numerical methods for singularly perturbed differential equations.

✦ Table of Contents

Front Matter....Pages I-XVIII
Front Matter....Pages 5-7
The Analytical Behaviour of Solutions....Pages 9-39
Numerical Methods for Second-Order Boundary Value Problems....Pages 41-149
Front Matter....Pages 151-153
Introduction....Pages 155-157
Analytical Behaviour of Solutions....Pages 159-168
Finite Difference Methods....Pages 169-194
Finite Element Methods....Pages 195-221
Two Adaptive Methods....Pages 223-229
Front Matter....Pages 231-233
Analytical Behaviour of Solutions....Pages 235-258
Finite Difference Methods....Pages 259-276
Finite Element Methods....Pages 277-425
Time-Dependent Problems....Pages 427-442
Front Matter....Pages 443-447
Existence and Uniqueness Results....Pages 449-452
Upwind Finite Element Method....Pages 453-463
Higher-Order Methods of Streamline Diffusion Type....Pages 465-484
Local Projection Stabilization for Equal-Order Interpolation....Pages 485-510
Local Projection Method for Inf-Sup Stable Elements....Pages 511-528
Mass Conservation for Coupled Flow-Transport Problems....Pages 529-543
Adaptive Error Control....Pages 545-549
Back Matter....Pages 551-604

✦ Subjects

Numerical Analysis;Appl.Mathematics/Computational Methods of Engineering;Mathematical Biology in General;Statistics for Life Sciences, Medicine, Health Sciences;Theoretical and Computational Chemistry;Mathematical Methods in Physics