Convection Diffusion Problems: An Introduction to Their Analysis and Numerical Solution (Graduate Studies in Mathematics) (Graduate Studies in Mathematics, 196) - Hardcover

Martin Stynes; David Stynes

Hardcover

ISBN 10: 1470448688 ISBN 13: 9781470448684

Publisher: American Mathematical Society, 2018

Synopsis

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.

About this title

About the Author

Martin Stynes: Beijing Computational Science Research Center, Beijing, China, David Stynes: Cork Institute of Technology, Cork, Ireland

Edition details

• Publisher: American Mathematical Society
• Publication date: 2018
• Language: English
• ISBN 10: 1470448688
• ISBN 13: 9781470448684
• Binding: Hardcover
• Number of pages: 156