Finite Elements and Fast Iterative Solvers: with Applications in Incompressible Fluid Dynamics

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ID: 295779
2005
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Abstract
Abstract 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.
Reference Key
openalex_W2133248904 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Howard C. Elman, David J. Silvester, Andrew J. Wathen
Journal Oxford University Press eBooks
Year 2005
DOI
10.1093/oso/9780198528678.001.0001
URL
https://doi.org/10.1093/oso/9780198528678.001.0001
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