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Damping due to continuum resonances can be calculated using dissipation-lessideal magnetohydrodynamics (MHD) provided that the poles due to theseresonances are properly treated. We describe a singular finite elementtechnique for calculating the continuum damping of Alfv\'{e}n waves. AFrobenius expansion is used to determine appropriate finite element basisfunctions 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 arecalculated iteratively using a Galerkin method. This method is used to find thecomplex frequency and mode structure of a toroidicity-induced Alfv\'{e}neigenmode (TAE) in a large aspect ratio circular tokamak and are shown to agreeclosely with a complex contour technique.

A singular finite element technique for calculating continuum damping of Alfv\'en eigenmodes