  As gravitational wave detectors improve in sensitivity, signal-to-noise
ratios of compact binary coalescences will dramatically increase, reaching
values in the hundreds and potentially thousands. Such strong signals offer
both exciting scientific opportunities and pose formidable challenges to the
template waveforms used for interpretation. Current waveform models are
informed by calibrating or fitting to numerical relativity waveforms and such
strong signals may unveil computational errors in generating these waveforms.
In this paper, we isolate a single source of computational error, that of the
finite grid resolution, and investigate its impact on parameter estimation for
aLIGO and Cosmic Explorer. We show that injecting a lower resolution simulation
tends to cause a downward shift in the recovered chirp mass and mass ratio
posteriors. We demonstrate that increasing the inclination angle or decreasing
the mass ratio raises the resolution required for unbiased parameter
estimation. We quantify the error associated with the highest-resolution
waveform utilized using an extrapolation procedure on the median of recovered
posteriors and confirm the accuracy of current waveforms for the synthetic
sources. We introduce a measure to predict the necessary numerical resolution
for unbiased parameter estimation and use it to predict that current waveforms
are suitable for equal and moderately unequal mass binaries for both detectors.
However, current waveforms fail to meet accuracy requirements for high
signal-to-noise ratio signals from highly unequal mass ratio binaries $(q
\lesssim 1/6)$, for all inclinations in Cosmic Explorer, and for high
inclinations in future updates to LIGO. Given that the resolution requirement
becomes more stringent with more unequal mass ratios, current waveforms may
lack the necessary accuracy, even at median signal-to-noise ratios for future
detectors.
