  Boundary integral numerical methods are among the most accurate methods for
interfacial Stokes flow, and are widely applied. They have the advantage that
only the boundary of the domain must be discretized, which reduces the number
of discretization points and allows the treatment of complicated interfaces.
Despite their popularity, there is no analysis of the convergence of these
methods for interfacial Stokes flow. In practice, the stability of
discretizations of the boundary integral formulation can depend sensitively on
details of the discretization and on the application of numerical filters. We
present a convergence analysis of the boundary integral method for Stokes flow,
focusing on a rather general method for computing the evolution of an elastic
capsule, viscous drop, or inviscid bubble in 2D strain and shear flows. The
analysis clarifies the role of numerical filters in practical computations.
