Convection-Diffusion Problems
An Introduction to Their Analysis and Numerical Solution
Seiten
2018
American Mathematical Society (Verlag)
978-1-4704-4868-4 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4868-4 (ISBN)
Provides a lucid yet thorough account of convection-dominated convection-diffusion problems and how to solve them numerically for beginning graduate students. The book includes a large number of exercises. An up-to-date bibliography provides the reader with further reading.
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.
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.
Martin Stynes, Beijing Computational Science Research Center, China. David Stynes, Cork Institute of Technology, Ireland.
Introduction and preliminary material
Convection-diffusion problems in one dimension
Finite difference methods in one dimension
Convection-diffusion problems in two dimensions
Finite difference methods in two dimensions
Finite element methods
Concluding remarks
Bibliography
Index
| Erscheinungsdatum | 10.12.2018 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Gewicht | 455 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Angewandte Mathematik |
| ISBN-10 | 1-4704-4868-8 / 1470448688 |
| ISBN-13 | 978-1-4704-4868-4 / 9781470448684 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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