  Many immersed boundary methods solve for surface stresses that impose the
velocity boundary conditions on an immersed body. These surface stresses may
contain spurious oscillations that make them ill-suited for representing the
physical surface stresses on the body. Moreover, these inaccurate stresses
often lead to unphysical oscillations in the history of integrated surface
forces such as the coefficient of lift. While the errors in the surface
stresses and forces do not necessarily affect the convergence of the velocity
field, it is desirable, especially in fluid-structure interaction problems, to
obtain smooth and convergent stress distributions on the surface. To this end,
we show that the equation for the surface stresses is an integral equation of
the first kind whose ill-posedness is the source of spurious oscillations in
the stresses. We also demonstrate that for sufficiently smooth delta functions,
the oscillations may be filtered out to obtain physically accurate surface
stresses. The filtering is applied as a post-processing procedure, so that the
convergence of the velocity field is unaffected. We demonstrate the efficacy of
the method by computing stresses and forces that converge to the physical
stresses and forces for several test problems.
