Kristoffer:

Is there a code that solves for example du/dx + du/dy = 0 with a DG formulation?

Yes, this is the advection equation, and you can find a DG solver in step-12 if you set the vector beta=[1,1] there.


I was wondering if there is any interest in creating a Space-Time DG method with deal.ii?

Yes, and people have done that. You might want to search for "space-time" in
  https://dealii.org/publications.html
to see a few examples. (Though I don't know whether they used DG methods.)

Best
 W.
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Wolfgang Bangerth          email:                 [email protected]
                           www: http://www.math.colostate.edu/~bangerth/

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