  In many numerical implementations of the Cauchy formulation of Einstein's
field equations one encounters artificial boundaries which raises the issue of
specifying boundary conditions. Such conditions have to be chosen carefully. In
particular, they should be compatible with the constraints, yield a well posed
initial-boundary value formulation and incorporate some physically desirable
properties like, for instance, minimizing reflections of gravitational
radiation.
  Motivated by the problem in General Relativity, we analyze a model problem,
consisting of a formulation of Maxwell's equations on a spatially compact
region of spacetime with timelike boundaries. The form in which the equations
are written is such that their structure is very similar to the
Einstein-Christoffel symmetric hyperbolic formulations of Einstein's field
equations. For this model problem, we specify a family of Sommerfeld-type
constraint-preserving boundary conditions and show that the resulting
initial-boundary value formulations are well posed. We expect that these
results can be generalized to the Einstein-Christoffel formulations of General
Relativity, at least in the case of linearizations about a stationary
background.
