New answers tagged discontinuous-galerkin
5
Pros:
With trigonometric basis functions your problem size is $N \text{log}(N)$ instead of $N^2$.
Stabilization techniques are easy to implement and cheap:
Filtering in the modal space.
Zero padding in the modal space.
No aliasing due to the Galerkin ansatz.
Energy/Entropy stable disctretizations, e.g. via a skew symmetric implementation, are quite easy.
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1
To expand on Wolfgang Bangerth's answer, I think P0 DG schemes reduce to two-point cell-centered finite volume schemes. I don't know if DG convergence analysis always includes $p = 0$, but the resulting finite volume schemes can be shown to converge under appropriate "mesh orthogonality" conditions.
https://math.unice.fr/~minjeaud/Donnees/...
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