A note on pressure accuracy in immersed boundary method for Stokes flow

In this short note, we provide a simplified one-dimensional analysis and two-dimensional numerical experiments to predict that the overall accuracy for the pressure or indicator function in immersed boundary calculations is first-order accurate in L1 norm, half-order accurate in L2 norm, but has O(1) error in L∞ norm. Despite the pressure has O(1) error near the interface, the velocity field still has the first-order convergence in immersed boundary calculations.