The New Jersey Institute of Technology's
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Title:	Convergence of the boundary integral method for interfacial stokes flow
Author:	Zhang, Keyang
View Online:	njit-etd2020-100 (viii, 96 pages ~ 0.6 MB pdf)
Department:	Department of Mathematical Sciences
Degree:	Doctor of Philosophy
Program:	Mathematical Sciences
Document Type:	Dissertation
Advisory Committee:	Siegel, Michael (Committee co-chair) Ambrose, David M. (Committee co-chair) Jiang, Shidong (Committee member) Boubendir, Yassine (Committee member) Hamfeldt, Brittany Froese (Committee member)
Date:	2020-12
Keywords:	Boundary integral method Interfacial flow Stokes flow
Availability:	Unrestricted
Abstract:	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.