Mostly Biomathematics Lunchtime Seminar

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The Regularised Immersed Boundary Method: A Numerical Analysis

Speaker: Alexandre Milewski, Courant Institute of Mathematical Sciences

Location: Warren Weaver Hall 1314

Date: Tuesday, April 28, 2026, 12:30 p.m.

Synopsis:

The immersed boundary (IB) method has been used as a means to simulate fluid-membrane interactions in a wide variety of biological and engineering applications. Although numerical convergence of the method has been empirically verified, it remains theoretically unproved, due to the singular forcing terms present in the governing equations. This talk is dedicated to a specific variant of the IB method, in which immersed structure is mollified in the continuous formulation. We utilise this fact to prove convergence of the IB method as applied to a moving, closed, 1D Hookean band immersed in a 2D Navier-Stokes fluid, commonly referred to as the Peskin problem.