Finite Elements and Fast Iterative Solvers: Paperback: Howard C. El
- Oxford University Press

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An excellent introduction to finite elements, iterative linear solvers and scientific computing

Contains theoretical problems and practical exercises

All methods and examples use freely available software

Focuses on theory and computation, not theory for computation

Describes approximation methods and numerical linear algebra

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 and 2); the convection-diffusion equation (chapters 3 and 4); the Stokes equations (chapters 5 and 6); and the Navier-Stokes equations (chapters 7 and 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, and a companion chapter concerned
with efficient iterative solution of the algebraic equations obtained from 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 fopr 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, it is an ideal teaching and learning resource.

Readership: Graduate students and researchers in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing.

Howard C. Elman, Department of Computer Science, University of Maryland, David J. Silvester, Department of Mathematics, UMIST, and Andrew J. Wathen, Oxford University Computing Laboratory

"...an excellent introduction to finite elements, iterative linear solvers and scientific computing for graduates in engineering, numerical analysis, applied mathematics and interdisciplinary scientific computing." - Adrian Carabineanu, Zentralblatt Math, Vol 1083

"The text offers a valuable contribution to all finite element researchers who would like to broaden both their fundamental and applied knowledge of the field." - Journal of Fluid Mechanics

Models of Incompressible Fluid Flow
The Poisson Equation
Solution of Discrete Poisson Problems
The Convection-Diffusion Equation
Solution of Discrete Convection-Diffusion Problems
The Stokes Equations
Solution of Discrete Stokes Problems
The Navier-Stokes Equations
Solution of Discrete Navier-Stokes Problems

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