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Finite Elements and Fast Iterative Solvers
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DOI：10.1093/acprof:oso/9780199678792.001.0001.png)
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AbstractThe subject of this book is the efficient solution of partial differential equations (PDEs) that arise when modelling incompressible fluid flow. The first part (Chapters 1 through 5) covers the Poisson equation and the Stokes equations. For each PDE, 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. Chapter 5 describes the basics of PDE-constrained optimization. The second part of the book (Chapters 6 to 11) is a more advanced introduction to the numerical analysis of incompressible flows. It starts with four chapters on the convection–diffusion equation and the steady Navier–Stokes equations, organized by equation with a chapter describing discretization coupled with a companion concerned with iterative solution algorithms. The book concludes with two chapters describing discretization and solution methods for models of unsteady flow and buoyancy-driven flow.
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