  We present first results obtained with a 3+1 dimensional adaptive mesh code
in numerical general relativity. The adaptive mesh is used in conjunction with
a standard ADM code for the evolution of a dynamically sliced Schwarzschild
spacetime (geodesic slicing). We argue that adaptive mesh is particularly
natural in the context of general relativity, where apart from adaptive mesh
refinement for numerical efficiency one may want to use the built in
flexibility to do numerical relativity on coordinate patches.
