The main advantage is that it reduces the Runge phenomenon and, it leads to faster convergence rates.
It also presents less numerical dispersion and need less nodes per wavelength (see 1 and 2). So, I would say that you would prefer the method for wave propagation scenarios.
Regarding software that includes SEM, I am aware of the following:
- FSELib: Matlab software accompanying the book Introduction to Finite and Spectral Element Methods using Matlab.
- Nektar: Spectral/HP FEM open code.
- RegSEM: used for seismic waves mainly.
- SPECFEM3D: used for seismic waves mainly.
References
Ainsworth, Mark, and Hafiz Abdul Wajid. "Dispersive and dissipative behavior of the spectral element method." SIAM Journal on Numerical Analysis 47.5 (2009): 3910-3937.
Guarín-Zapata, Nicolás, and Juan Gomez. "Evaluation of the spectral finite element method with the theory of phononic crystals." Journal of Computational Acoustics 23.02 (2015): 1550004.