> This could be useful to solve Euler equation with a DG method that
> employs a Riemann solver to compute the numerical fluxes
> (discontinuous at element faces-edges) without dealing with Godunov
> fluxes to compute the jacobian... Am I wrong?

Absolutely.  And a common trick from the finite volume community would be to
precondition with a first-order implicit system operator, while you evaluate
the residual to higher order.  In DG this equates to piecewise constant,

For perfect gas in 3D this would give you 5*n_cells*n_faces_per_cell
(assuming all your elements have the same number of faces) storage for the
preconditioner instead of (5*n_cells*n_faces_per_cell*n_dofs_per_var)

-Ben



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