Details
Robust Numerical Methods for Singularly Perturbed Differential Equations
Convection-Diffusion-Reaction and Flow ProblemsSpringer Series in Computational Mathematics, Band 24 2nd ed. 2008
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160,49 € |
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| Verlag: | Springer |
| Format: | |
| Veröffentl.: | 17.09.2008 |
| ISBN/EAN: | 9783540344674 |
| Sprache: | englisch |
| Anzahl Seiten: | 604 |
Dieses eBook enthält ein Wasserzeichen.
Beschreibungen
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.
<P>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.</P>
<p>Includes supplementary material: sn.pub/extras</p>
Beginning with ordinary differential equations, then moving on to parabolic and elliptic problems and culminating with the Navier-Stokes equations, the reader is led through the theoretical and practical aspects of the most important methods used to compute numerical solutions for singular perturbation problems.
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