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OverviewMany 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. Full Product DetailsAuthor: Martin Stynes , David StynesPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.455kg ISBN: 9781470448684ISBN 10: 1470448688 Pages: 156 Publication Date: 30 December 2018 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsIntroduction 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 Bibliography IndexReviewsAuthor InformationMartin Stynes, Beijing Computational Science Research Center, China. David Stynes, Cork Institute of Technology, Ireland. Tab Content 6Author Website:Countries AvailableAll regions |