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Convection-diffusion problems : an introduction to their analysis and numerical solution

Author: M Stynes; David Stynes
Publisher: Providence, Rhode Island : American Mathematical Society ; Halifax, Nova Scotia, Canada : Atlantic Association for Research in the Mathematical Sciences, [2018]
Series: Graduate studies in mathematics, v. 196.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Stynes, M. (Martin), 1951-
Convection-diffusion problems.
Providence, Rhode Island : American Mathematical Society ; Halifax, Nova Scotia, Canada : Atlantic Association for Research in the Mathematical Sciences, [2018]
(DLC) 2018035503
(OCoLC)1048658261
Print version:
(DLC) 2018035503
(OCoLC)1048658261
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: M Stynes; David Stynes
ISBN: 9781470450212 1470450216
OCLC Number: 1078949449
Description: 1 online resource.
Contents: Cover; Title page; Preface; Chapter 1. Introduction and Preliminary Material; 1.1. A simple example; 1.2. A little motivation and history; 1.3. Notation; 1.4. Maximum principle and barrier functions; 1.5. Asymptotic expansions; Chapter 2. Convection-Diffusion Problems in One Dimension; 2.1. Asymptotic analysis-an extended example; 2.2. Green's functions; 2.3. A priori bounds on the solution and its derivatives; 2.4. Decompositions of the solution; Chapter 3. Finite Difference Methods in One Dimension; 3.1. M-matrices, upwinding; 3.2. Artificial diffusion; 3.3. Uniformly convergent schemes 3.4. Shishkin meshesChapter 4. Convection-Diffusion Problems in Two Dimensions; 4.1. General description; 4.2. A priori estimates; 4.3. General comments on numerical methods; Chapter 5. Finite Difference Methods in Two Dimensions; 5.1. Extending one-dimensional approaches; 5.2. Shishkin meshes; 5.3. Characteristic boundary layers; 5.4. Other remarks; Chapter 6. Finite Element Methods; 6.1. The loss of stability in the (Bubnov-)Galerkin FEM; 6.2. Relationship to classical FEM analysis; 6.3. *-splines; 6.4. The streamline-diffusion finite element method (SUPG) 6.5. Stability of the Galerkin FEM for higher-degree polynomials6.6. Shishkin meshes; 6.7. Discontinuous Galerkin finite element method; 6.8. Continuous interior penalty (CIP) method; 6.9. Adaptive methods; Chapter 7. Concluding Remarks; Bibliography; Index; Back Cover
Series Title: Graduate studies in mathematics, v. 196.
Responsibility: Martin Stynes, David Stynes.

Abstract:

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  Read more...

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