An analysis of the regularized stokeslet method ⋆

A regularized boundary integral equation for exterior Stokes flow around rigid bodies in three dimensions is studied. The formulation is based on a free-space solution of the Stokes equations with concentrated, but smooth forcing and involves two regularization parameters that control the behavior of the free-space solution and the conditioning of the integral equation. The smooth free-space solution is known as a regularized stokeslet and has been employed by various authors in the numerical treatment of Stokes flow problems. Convergence theorems are established for the regularization error associated with the formulation and for the discretization error associated with its subsequent numerical approximation by Nyström methods. The results show that the overall method provides a convergent approximation of the Stokes equations as the regularization and discretization parameters are refined along suitable paths.