Some mathematical problems in numerical relativity
  The main goal of numerical relativity is the long time simulation of highly nonlinear spacetimes that cannot be treated by perturbation theory. This involves analytic, computational and physical issues. At present, the major impasses to achieving global simulations of physical usefulness are of an analytic/computational nature. We present here some examples of how analytic insight can lend useful guidance for the improvement of numerical approaches. 
Maria Babiuc, Bela Szilagyi, Jeffrey Winicour