Document Type


Date of Award


Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Michael Siegel

Second Advisor

David M. Ambrose

Third Advisor

Shidong Jiang

Fourth Advisor

Yassine Boubendir

Fifth Advisor

Brittany Froese Hamfeldt


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. A convergence analysis of the boundary integral method for Stokes flow is presented focusing on a variant of the method of [22] for computing the evolution of an elastic capsule in two dimensional strain and shear flows. The analysis clarifies the role of numerical filters in practical computations.



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