Sale!

Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Edition by Martin Stynes, David Stynes 1470448688 978-1470448684

Name: Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Edition by Martin Stynes, David Stynes 1470448688 978-1470448684
SKU: EB-34099534
Availability: InStock

Original price was: $50.00.Current price is: $25.00.

Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Edition Martin Stynes Digital Instant Download

Author(s): Martin Stynes, David Stynes

ISBN(s): 9781470448684, 1470448688

Edition: 1

File Details: DJVU, 1.78 MB

Year: 2018

Language: English

SKU: EB-34099534 Category: Mathematics Tags: David Stynes, Martin Stynes

Description

Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Edition by Martin Stynes, David Stynes – Ebook PDF Instant Download/Delivery: 1470448688, 978-1470448684

Full download Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Edition after payment

Product details:

ISBN 10: 1470448688

ISBN 13: 978-1470448684

Author: Martin Stynes, David Stynes

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.

Convection Diffusion Problems An Introduction to Their Analysis and Numerical Solution 1st Table of contents:

Chapter 1: Introduction and Preliminary Material

1.1. A Simple Example
1.2. Motivation and Historical Background
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. Decomposition of the Solution

Chapter 3: Finite Difference Methods in One Dimension

3.1. M-Matrices and Upwinding
3.2. Artificial Diffusion
3.3. Uniformly Convergent Schemes
3.4. Shishkin Meshes

Chapter 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. Additional Remarks

Chapter 6: Finite Element Methods

6.1. Stability Challenges in the (Bubnov-) Galerkin FEM
6.2. Relationship to Classical FEM Analysis
6.3. *-Splines
6.4. Streamline-Diffusion Finite Element Method (SUPG)
6.5. Stability of Galerkin FEM for Higher-Degree Polynomials
6.6. Shishkin Meshes
6.7. Discontinuous Galerkin Finite Element Method
6.8. Continuous Interior Penalty (CIP) Method
6.9. Adaptive Methods