Programming of Finite Element Solvers

Abstract

The present chapter explains the usage of the finite element toolbox in Diffpack. The model problems are kept quite simple in order to concentrate on programming details. In Chapters 3.1–1.7 we deal with the Poisson equation. A trivial extension to the convection-diffusion equation is exemplified in Chapter 3.8. Chapters 3.9 and 3.10 demonstrate that only minor extensions of the Poisson equation solvers are needed to handle time-dependent problems, in this case the heat equation. Finally, Chapter 3.11 brings in some new tools for particularly efficient solution of PDEs with time-independent coefficients. The required background for working with this chapter is knowledge of the finite element method (at least the material corresponding to Chapters 2.1–2.7) and basic concepts in C++ and Diffpack (at least Chapters 1.1–1.3, 1.5.1–1.5.3, and 1.5.5; Chapter 1.6 is also useful).