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Numerical solution of convection-diffusion problems. (English) Zbl 0861.65070
Applied Mathematics and Mathematical Computation. 12. London: Chapman & Hall. xii, 372 p. (1996).
This book gives a comprehensive survey of numerical methods for singularly-perturbed convection-diffusion equations. The emphasis is on methods which remain effective when convection becomes dominant. The book begins with practical examples of singular perturbation problems and explains why traditional numerical methods are ineffective for them. Most of the rest of the book is devoted to robust methods for steady-state problems, with incompressible fluid flow as the predominant application. The advantages of upwind finite element and finite volume schemes are explained clearly and convincingly. The final chapter deals with time-dependent problems, mainly for compressible fluids. Here, the methods of choice are different, particularly if one wishes to locate and model shocks. In summary, this field of research is currently very active, and this book is an excellent introduction.

MSC:
65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
76-02 Research exposition (monographs, survey articles) pertaining to fluid mechanics
65Nxx Numerical methods for partial differential equations, boundary value problems
76Mxx Basic methods in fluid mechanics
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