Abstract
Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, uid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is rst order accurate in the L 1 norm. But almost no rigorous proof could be found in the literature until recently [14] in which the author showed that the velocity is indeed rst order accurate for the Stokes equations with a periodic boundary condition. In this paper, we show rst order convergence with a log h factor of the IB method for elliptic interface problems essentially without the boundary condition restrictions. The results should be applicable to the IB method for many dieren t situations involving elliptic solvers for Stokes and Navier-Stokes equations.
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