Galerkin Boundary Elements for Exterior Stokes Flows

Abstract

An indirect boundary integral equation for steady Stokes flow around a rigid body in the three-dimensional space is proposed, and is numerically solved by using collocation and Galerkin weight- ing procedures. The resulting double surface integrals of the Galerkin technique that express the pairwise interaction among all boundary elements, which are quadruple integrals, are computed on flat simplex triangles using a regularized quadrature scheme. Numerical examples include the steady creeping flow around the sphere of unit radius and the cube of unit edge length, covering issues on the convergence under mesh refinement and stability under small mesh perturbations.