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Convection-Diffusion Problems: An Introduction to Their Analysis and Numerical Solution

Martin Stynes Beijing Computational Science Research Center, Beijing, China
David Stynes Cork Institute of Technology, Cork, Ireland
Available Formats:
Hardcover ISBN: 978-1-4704-4868-4
Product Code: GSM/196
List Price: $83.00 MAA Member Price:$74.70
AMS Member Price: $66.40 Electronic ISBN: 978-1-4704-5021-2 Product Code: GSM/196.E List Price:$83.00
MAA Member Price: $74.70 AMS Member Price:$66.40
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List Price: $124.50 MAA Member Price:$112.05
AMS Member Price: $99.60 Click above image for expanded view Convection-Diffusion Problems: An Introduction to Their Analysis and Numerical Solution Martin Stynes Beijing Computational Science Research Center, Beijing, China David Stynes Cork Institute of Technology, Cork, Ireland Available Formats:  Hardcover ISBN: 978-1-4704-4868-4 Product Code: GSM/196  List Price:$83.00 MAA Member Price: $74.70 AMS Member Price:$66.40
 Electronic ISBN: 978-1-4704-5021-2 Product Code: GSM/196.E
 List Price: $83.00 MAA Member Price:$74.70 AMS Member Price: $66.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$124.50 MAA Member Price: $112.05 AMS Member Price:$99.60
• Book Details

Volume: 1962018; 156 pp
MSC: Primary 65; Secondary 34; 35;

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.

Graduate students and researchers interested in singular perturbation theory and appropriate numerical methods.

• Chapters
• 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

• Reviews

• This book was written for those having some familiarity with numerical methods and their analysis who wish to investigate convection-diffusion problems. It is a well-written text best suited to readers who are interested in pursuing challenging problems in convection-diffusion and who have at least a modest background in partial differential equations and their numerical solution.

Bill Satzer, MAA Reviews
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 1962018; 156 pp
MSC: Primary 65; Secondary 34; 35;

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.

Graduate students and researchers interested in singular perturbation theory and appropriate numerical methods.

• Chapters
• 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
• This book was written for those having some familiarity with numerical methods and their analysis who wish to investigate convection-diffusion problems. It is a well-written text best suited to readers who are interested in pursuing challenging problems in convection-diffusion and who have at least a modest background in partial differential equations and their numerical solution.

Bill Satzer, MAA Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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