Convergence of the boundary integral method for interfacial Stokes flow
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- Math. Comp. 92 (2023), 695-748 Request permission
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. We present a convergence analysis of the boundary integral method for Stokes flow, focusing on a rather general method for computing the evolution of an elastic capsule or viscous drop in 2D strain and shear flows. The analysis clarifies the role of numerical filters in practical computations.References
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Additional Information
- David M. Ambrose
- Affiliation: Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 09104
- MR Author ID: 720777
- ORCID: 0000-0003-4753-0319
- Email: ambrose@math.drexel.edu
- Michael Siegel
- Affiliation: Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102
- MR Author ID: 294740
- Email: misieg@njit.edu
- Keyang Zhang
- Affiliation: Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, New Jersey 07102
- Email: kz78@njit.edu
- Received by editor(s): May 13, 2021
- Received by editor(s) in revised form: May 10, 2022
- Published electronically: November 15, 2022
- Additional Notes: The first author was supported by NSF grant DMS-1907684. The second author was supported by NSF grant DMS-1909407.
The second author is the corresponding author. - © Copyright 2022 American Mathematical Society
- Journal: Math. Comp. 92 (2023), 695-748
- MSC (2020): Primary 65N38, 76T06
- DOI: https://doi.org/10.1090/mcom/3787
- MathSciNet review: 4524106