Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp quadrature error bounds for the nearest-neighbor discretization of
  the regularized stokeslet boundary integral equation   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.

9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci