A current problem that I am working on requires me to compute the solution from the heat diffusion evolution on a discontinuous function. More precisely - I have a Delaunay triangulation and within each triangle a polynomial function is defined such that it can be discontinuous at the edges. For a constant function within each triangle the two-point flux approximation scheme is applicable (precisely because I have a Delaunay triangulation).

Is there a DG extension/analogue to such a cell-centered scheme? I would like to be able to use a similar cell-centered scheme on cells with higher polynomial degrees.

To put it simply, I am looking for a (simpler) method to perform homogeneous diffusion on a mesh where discontinuous polynomial functions are defined within each cell (preferably one that extends to higher degree polynomials unlike the FVM scheme that I mentioned).

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    $\begingroup$ There is a vast literature on DG methods for diffusion pde. E.g., (1) doi.org/10.1137/1.9780898717440 (mostly about interior penalty methods) (2) DOI:10.1007/978-3-319-19267-3 (3) DOI:10.1007/978-3-642-22980-0 $\endgroup$ – cfdlab Jun 28 '20 at 3:53
  • $\begingroup$ @cfdlab Great book! Thank you for recommending it. $\endgroup$ – lightxbulb Jun 28 '20 at 9:05

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