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

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…