Problems and Successes in the Numerical Approach to the Conformal Field Equations

This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at the AEI in the last years, and discuss a milestone result obtained by Hübner. Then we present more recent results as examples to sketch the problems we face in the conformal approach to numerical relativity and outline a possible roadmap toward making this approach a practical tool