To study a physically motivated PDE model, it often helps to compute a numerical solution to get a sense of how the analytical solution would behave for a certain set of initial and boundary conditions. For a numerical solution to be meaningful, however, one has to ensure that over many iterations of a reasonable time step size, the numerical solution converges to the analytical solution. In this talk, I will introduce one of the most popular methods to compute interfacial fluid flow in fluid mechanics called the boundary integral (BI) method and illustrate how one may show that a boundary-integral type numerical scheme converges to an analytical solution for a two-phase Stokes flow problem.