Convergence of the boundary integral method for interfacial Stokes flow

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