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We present results of 3D numerical simulations using a finite difference codefeaturing fixed mesh refinement (FMR), in which a subset of the computationaldomain is refined in space and time. We apply this code to a series of testcases including a robust stability test, a nonlinear gauge wave and an excisedSchwarzschild black hole in an evolving gauge. We find that the mesh refinementresults are comparable in accuracy, stability and convergence to unigridsimulations with the same effective resolution. At the same time, the use ofFMR reduces the computational resources needed to obtain a given accuracy.Particular care must be taken at the interfaces between coarse and fine gridsto avoid a loss of convergence at higher resolutions, and we introduce the useof "buffer zones" as one resolution of this issue. We also introduce a newmethod for initial data generation, which enables higher-order interpolation intime even from the initial time slice. This FMR system, "Carpet", is a drivermodule in the freely available Cactus computational infrastructure, and is ableto endow generic existing Cactus simulation modules ("thorns") with FMR withlittle or no extra effort.Comment: 20 pages, 15 figures; published version, but with colour figure

Evolutions in 3D numerical relativity using fixed mesh refinement