  I consider the initial-boundary-value-problem of nonlinear general
relativistic vacuum spacetimes, which today cannot yet be evolved numerically
in a satisfactory manner. Specifically, I look at gauge conditions, classifying
them into gauge evolution conditions and gauge fixing conditions. In this
terminology, a gauge fixing condition is a condition that removes all gauge
degrees of freedom from a system, whereas a gauge evolution condition
determines only the time evolution of the gauge condition, while the gauge
condition itself remains unspecified. I find that most of today's gauge
conditions are only gauge evolution conditions.
  I present a system of evolution equations containing a gauge fixing
condition, and describe an efficient numerical implementation using constrained
evolution. I examine the numerical behaviour of this system for several test
problems, such as linear gravitational waves or nonlinear gauge waves. I find
that the system is robustly stable and second-order convergent. I then apply it
to more realistic configurations, such as Brill waves or single black holes,
where the system is also stable and accurate.
