Basic Theory of Partial Differential Equations and Their Discretization

Abstract

In this chapter we present some basic elements of the analysis of partial differential equations, and of their numerical discretization by finite differences. Our aim is to introduce some notions that enable the reader to follow the material developed in the subsequent chapters. Both the analysis and the numerical solution of partial differential equations (PDEs) are research areas by themselves, with a large amount of related literature. We refer, for instance, to the books [9,19] for the analysis of PDEs and to, e.g., [23, 52] for their numerical approximation.