The main advantage is that it reduces the Runge phenomenon and 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](http://dehesa.freeshell.org/FSELIB/): Matlab software accompanying the book Introduction to Finite and Spectral Element Methods using Matlab.
- [Nektar](https://www.nektar.info): Spectral/HP FEM open code.
- [RegSEM](http://www.ipgp.fr/~paulcup/RegSEM.html): used for seismic waves mainly.
- [SPECFEM3D](https://geodynamics.org/cig/software/specfem3d/): used for seismic waves mainly.



## References

1. 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.


2. 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.