Robust Numerical Methods for Singularly Perturbed Differential Equations Convection-Diffusion-Reaction and Flow Problems
Title:
Robust Numerical Methods for Singularly Perturbed Differential Equations Convection-Diffusion-Reaction and Flow Problems
Author:
Roos, Hans-Görg. author.
ISBN:
9783540344674
Personal Author:
Edition:
2.
Physical Description:
XIV, 604 p. 41 illus. online resource.
Series:
Springer Series in Computational Mathematics, 24
Contents:
Ordinary Differential Equations -- The Analytical Behaviour of Solutions -- Numerical Methods for Second-Order Boundary Value Problems -- Parabolic Initial-Boundary Value Problems in One Space Dimension -- Analytical Behaviour of Solutions -- Finite Difference Methods -- Finite Element Methods -- Two Adaptive Methods -- Elliptic and Parabolic Problems in Several Space Dimensions -- Analytical Behaviour of Solutions -- Finite Difference Methods -- Finite Element Methods -- Time-Dependent Problems -- The Incompressible Navier-Stokes Equations -- Existence and Uniqueness Results -- Upwind Finite Element Method -- Higher-Order Methods of Streamline Diffusion Type -- Local Projection Stabilization for Equal-Order Interpolation -- Local Projection Method for Inf-Sup Stable Elements -- Mass Conservation for Coupled Flow-Transport Problems -- Adaptive Error Control.
Abstract:
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.
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Added Corporate Author:
Electronic Access:
http://dx.doi.org/10.1007/978-3-540-34467-4