Electrostatics with MaxFEM

In this chapter we deal with the numerical solution of some electrostatics problems by using MaxFEM. The aim is to show a set of numerical simulations to illustrate the concepts of electric field and electric potential. The chapter begins with a review of some classical problems with analytical solution appearing in the vast majority of textbooks. These are limited to situations where the geometry is especially simple and maps onto a standard coordinate system, more specifically, cartesian, cylindrical or spherical coordinates. Some of these analytical examples deal with situations that are never encountered in practice (for instance, those where the geometry is “infinite” in some direction). However, they appear in the classical literature in electromagnetism since they are excellent approximations to some real systems. The second part proposes problems oriented to physical applications where a numerical approach is necessary or simpler than an analytical one. We refer the reader to Chap. 7 and Sect. 7.4 for information about the mathematical model and the weak formulation of electrostatics problems, respectively.