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Numerical relativity became a powerful tool to investigate the dynamics ofbinary problems with black holes or neutron stars as well as the very structureof General Relativity. Although public numerical relativity codes are availableto evolve such systems, a proper understanding of the methods involved is quiteimportant. Here we focus on the numerical solution of elliptic partialdifferential equations. Such equations arise when preparing initial data fornumerical relativity, but also for monitoring the evolution of black holes.Because such elliptic equations play an important role in many branches ofphysics, we give an overview of the topic, and show how to numerically solvethem with simple examples and sample codes written in C++ and Fortran90 forbeginners in numerical relativity or other fields requiring numericalexpertise.

Initial Conditions for Numerical Relativity -- Introduction to numerical methods for solving elliptic PDEs