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

When convection dominates diffusion, special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book, and finite-difference and finite element methods are presented.

Format: Hardback
Length: 156 pages
Publication date: 30 December 2018
Publisher: American Mathematical Society

Numerous physical issues entail diffusive and convective (transport) processes. Standard numerical approaches are adequate when diffusion predominates convection. However, the conventional approaches become unstable when convection predominates diffusion, necessitating the use of specialized techniques to compute precise numerical approximations of the unknown solution. This convection-dominated regime is the book's main emphasis. After thoroughly examining the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and develop numerical methods specifically tailored to this class of challenges. They initially explore finite-difference methods for two-point boundary value problems, as their analysis requires minimal theoretical background. Upwinding, artificial diffusion, uniformly convergent methods, and Shishkin meshes are some of the topics covered. Throughout, the authors prioritize the accuracy of solutions when the diffusion coefficient is near zero. Later in the book, they focus on finite element methods for one- and two-dimensional problems. This comprehensive yet accessible account of convection-dominated convection-diffusion problems and their numerical solution is intended for beginning graduate students, and it includes a substantial number of exercises. An up-to-date bibliography provides the reader with additional reading. This book is published in cooperation with the Atlantic Association for Research in the Mathematical Sciences.

Dimension: 254 x 178 (mm)
ISBN-13: 9781470448684