  Damping due to continuum resonances can be calculated using dissipation-less
ideal magnetohydrodynamics (MHD) provided that the poles due to these
resonances are properly treated. We describe a singular finite element
technique for calculating the continuum damping of Alfv\'{e}n waves. A
Frobenius expansion is used to determine appropriate finite element basis
functions on an inner region surrounding a pole due to the continuum resonance.
The location of the pole due to the continuum resonance and mode frequency are
calculated iteratively using a Galerkin method. This method is used to find the
complex frequency and mode structure of a toroidicity-induced Alfv\'{e}n
eigenmode (TAE) in a large aspect ratio circular tokamak and are shown to agree
closely with a complex contour technique.

Plasma Physics