Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics (Numerical Mathematics and Scientific Computation) - Hardcover

Elman, Howard C.; Silvester, David J.; Wathen, Andrew J.

9780198528678: Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics (Numerical Mathematics and Scientific Computation)

Hardcover

ISBN 10: 0198528671 ISBN 13: 9780198528678

Publisher: OUP Oxford, 2005

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The subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The material is organized into four groups of two chapters each, covering the Poisson equation (chapters 1 & 2); the convection-diffucion equation
(chapters 3 & 4); the Stokes equations (chapters 5 & 6); and the Navier-Stokes equations (chapters 7 & 8). These equations represent important models within the domain of computational fluid dynamics, but they also arise in many other settings. For each PDE model, there is a chapter concerned with
finite element discretization. For each problem and associated solvers there is a description of how to compute along with theoretical analysis which guides the choice of approaches. Illustrative numerical results occur throughout the book, which have been computed with the freely downloadable
IFISS software. All numerical results should be reproducible by readers who have access to MATLAB and there is considerable scope for experimentation in the 'computational laboratory' provided by the software. This book provides an excellent introduction to finite elements, iterative linear solvers
and scientific computing aimed at graduates in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing. Including theoretical problems and practical exercises closely tied with freely downloadable MATLAB software, this book is an ideal teaching and learning
resource.

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Review

The authors' intended audience is at the level of graduate students and researchers, and we believe that the text offers a valuable contribution to all finite element researchers who would like to broadened both their fundamental and applied knowledge of the field. (Spencer J. Sherwin and Robert M. Kirby, Fluid Mechanics, Vol 557, 2006)