Hi all,

I am doing an operator-splitting time-stepping scheme for an advection-diffusion-reaction system. That said, I have two maybe related questions.

1) I see that you guys have a nice low order DG scheme for the advection equation, and was wondering if a similar discretization can be made for the transient diffusion equation.

I have seen plenty of nodally discontinuous galerkin methods like SIPG, but is it possible to discretize that equation using DG0 elements (i.e., piece-wise constant)? In other words, I am wondering if it’s possible to come up with a finite-volume-like weak form of the following:

du/dt - div(D*grad(u)) = f

where D is the diffusivity tensor (dim by dim) and we use backward euler time-stepping.

2) Suppose I use the DG0 formulation for advection and CG1 for diffusion, in operator splitting, the “initial condition” for one operator is the computed solution from the previous operator. That is, if I first solve the advection equation for one time step, that solution becomes the initial condition for the diffusion equation. If I have to pass back and forth between DG0 and CG1 solution spaces, will I lose a lot of accuracy due to projecting or “smoothening” out the data?

Thanks,
Justin
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