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Convection-Diffusion Problems - An Introduction to Their Analysis and Numerical Solution (Hardcover)
Loot Price: R1,765
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Convection-Diffusion Problems - An Introduction to Their Analysis and Numerical Solution (Hardcover)
Series: Graduate Studies in Mathematics
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Many physical problems involve diffusive and convective (transport)
processes. When diffusion dominates convection, standard numerical
methods work satisfactorily. But when convection dominates
diffusion, the standard methods become unstable, and special
techniques are needed to compute accurate numerical approximations
of the unknown solution. This convection-dominated regime is the
focus of the book. After discussing at length the nature of
solutions to convection-dominated convection-diffusion problems,
the authors motivate and design numerical methods that are
particularly suited to this class of problems. At first they
examine finite-difference methods for two-point boundary value
problems, as their analysis requires little theoretical background.
Upwinding, artificial diffusion, uniformly convergent methods, and
Shishkin meshes are some of the topics presented. Throughout, the
authors are concerned with the accuracy of solutions when the
diffusion coefficient is close to zero. Later in the book they
concentrate on finite element methods for problems posed in one and
two dimensions. This lucid yet thorough account of
convection-dominated convection-diffusion problems and how to solve
them numerically is meant for beginning graduate students, and it
includes a large number of exercises. An up-to-date bibliography
provides the reader with further reading. This book is published in
cooperation with Atlantic Association for Research in the
Mathematical Sciences.
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