Finite Elements and Fast Iterative Solvers

Abstract The 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.