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

Abstract

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 L(1) norm, half-order accurate in L(2) norm, but has O(1) error in L(infinity) Despite the pressure has O(1) error near the interface, the velocity field still has the first-order convergence in immersed boundary calculations. (C) 2011 Elsevier Inc. All rights reserved.