  Numerical relativity became a powerful tool to investigate the dynamics of
binary problems with black holes or neutron stars as well as the very structure
of General Relativity. Although public numerical relativity codes are available
to evolve such systems, a proper understanding of the methods involved is quite
important. Here we focus on the numerical solution of elliptic partial
differential equations. Such equations arise when preparing initial data for
numerical relativity, but also for monitoring the evolution of black holes.
Because such elliptic equations play an important role in many branches of
physics, we give an overview of the topic, and show how to numerically solve
them with simple examples and sample codes written in C++ and Fortran90 for
beginners in numerical relativity or other fields requiring numerical
expertise.
