  Continuum resonance damping is an important factor in determining the
stability of certain global modes in fusion plasmas. A number of analytic and
numerical approaches have been developed to compute this damping, particularly
in the case of the toroidicity-induced shear Alfv\'en eigenmode. This paper
compares results obtained using an analytical perturbative approach with those
found using resistive and complex contour numerical approaches. It is found
that the perturbative method does not provide accurate agreement with reliable
numerical methods for the range of parameters examined. This discrepancy exists
even in the limit where damping approaches zero. When the perturbative
technique is implemented using a standard finite element method, the damping
estimate fails to converge with radial grid resolution. The finite elements
used cannot accurately represent the eigenmode in the region of the continuum
resonance, regardless of the number of radial grid points used.
