Lp Convergence of the Immersed Boundary Method for Stationary Stokes Problems

In this paper, we analyze the convergence of the immersed boundary (IB) method as applied to a static Stokes flow problem. Using estimates obtained in [5], we consider a problem in which a d-dimensional structure is immersed in n-dimension, and prove error estimates for both the pressure and the velocity field in the Lp(1 ≤ p ≤ ∞) norm. One interesting consequence of our analysis is that the asymptotic error rates in the L1 norm do not depend on either d or n and in the Lp (p > 1) norm they only depend on n − d. The resulting estimates are checked numerically for optimality.