Evolving a puncture black hole with fixed mesh refinement

We present an algorithm for treating mesh refinement interfaces in numerical relativity. We discuss the behavior of the solution near such interfaces located in the strong-field regions of dynamical black hole spacetimes, with particular attention to the convergence properties of the simulations. In our applications of this technique to the evolution of puncture initial data with vanishing shift, we demonstrate that it is possible to simultaneously maintain second order convergence near the puncture and extend the outer boundary beyond $100M$, thereby approaching the asymptotically flat region in which boundary condition problems are less difficult and wave extraction is meaningful.