  I discuss the accuracy requirements on numerical relativity calculations of
inspiraling compact object binaries whose extracted gravitational waveforms are
to be used as templates for matched filtering signal extraction and physical
parameter estimation in modern interferometric gravitational wave detectors.
Using a post-Newtonian point particle model for the pre-merger phase of the
binary inspiral, I calculate the maximum allowable errors for the mass and
relative velocity and positions of the binary during numerical simulations of
the binary inspiral. These maximum allowable errors are compared to the errors
of state-of-the-art numerical simulations of multiple-orbit binary neutron star
calculations in full general relativity, and are found to be smaller by several
orders of magnitude. A post-Newtonian model for the error of these numerical
simulations suggests that adaptive mesh refinement coupled with second order
accurate finite difference codes will {\it not} be able to robustly obtain the
accuracy required for reliable gravitational wave extraction on Terabyte-scale
computers. I conclude that higher order methods (higher order finite difference
methods and/or spectral methods) combined with adaptive mesh refinement and/or
multipatch technology will be needed for robustly accurate gravitational wave
extraction from numerical relativity calculations of binary coalescence
scenarios.
