  The method of regularized stokeslets is a powerful numerical method to solve
the Stokes flow equations for problems in biological fluid mechanics. A recent
variation of this method incorporates a nearest-neighbor discretization to
improve accuracy and efficiency while maintaining the ease-of-implementation of
the original meshless method. This method contains three sources of numerical
error, the regularization error associated from using the regularized form of
the boundary integral equations (with parameter $\varepsilon$), and two sources
of discretization error associated with the force and quadrature
discretizations (with lengthscales $h_f$ and $h_q$). A key issue to address is
the quadrature error: initial work has not fully explained observed numerical
convergence phenomena. In the present manuscript we construct sharp quadrature
error bounds for the nearest-neighbor discretisation, noting that the error for
a single evaluation of the kernel depends on the smallest distance ($\delta$)
between these discretization sets. The quadrature error bounds are described
for two cases: with disjoint sets ($\delta>0$) being close to linear in $h_q$
and insensitive to $\varepsilon$, and contained sets ($\delta=0$) being
quadratic in $h_q$ with inverse dependence on $\varepsilon$. The practical
implications of these error bounds are discussed with reference to the
condition number of the matrix system for the nearest-neighbor method, with the
analysis revealing that the condition number is insensitive to $\varepsilon$
for disjoint sets, and grows linearly with $\varepsilon$ for contained sets.
Error bounds for the general case ($\delta\geq 0$) are revealed to be
proportional to the sum of the errors for each case.
