[ChopraAbhi]

I'm interested in the applying time spectral method to the discontinuous-galerkin finite element based CFD (https://pdfs.semanticscholar.org/618...0f7a92b1d2.pdf). I came across a spectral element method and was wondering if it has the time spectral component in it?

[Eifoehn4]

Could you rephrase your question or be more specific?

[ChopraAbhi]

Sorry for not being clear. I was wondering if in spectral element method, does the time discritization takes the form of time spectral method described in the above paper? Is there something like pseudo-spectral method where space discritization is done in galerkin / DG framework and time can be done in spectral framework? Whatever paper I have read usually does time spectral in FVM (mainly) or FDM, not came across implementation in FEM. I hope I'm clear this time.

[Eifoehn4]

The time discretization you mentioned in the paper is not standard at all and quite specific.

Generally explicit discretizations of spectral collocation/Galerkin (continuous or discontinuous) methods are equiped with one-step methods like Runge-Kutta (strong-stability preserving and/or low storage) or multi-step methods like Adams–Bashforth.
Moreover there are some groups which apply the idea of Lax-Wendroff or Cauchy-Kovalevskaya by using a space-time Taylor polynomial. This results in e.g. ADER-DG methods.

Regards