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I am aware that both FEniCS and deal.ii are capable of solving problems with Discontinuous Galerkin (DG) method. I would like to specifically know if any of these two softwares can cater these requirements. Other software suggestions are also welcome; I am aware of these two because they are actively developed. I am specifically interested in solving hyperbolic (wave-dominated) problems.

  1. Local DG implementation
  2. User defined numerical flux function.
  3. Access and modify nodal/modal basis function coefficients. This is required because I want to implement limiters (for shock capturing).
  4. Support for both structured and unstructured meshes.

I request FEniCS/deal.ii users to kindly answer.

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    $\begingroup$ There is the DUNE / DUNE PDELAB ecosystem, where some DG methods are already implemented, but I can't really recommend them for lack of Documentation. If I where you, I would go with whatever package has the most active users and the best documentation. That might influence your overall productivity more than minor differences in the implementations. (my 2 cents) $\endgroup$
    – MPIchael
    Jun 25, 2019 at 10:14
  • $\begingroup$ I would also take into account the type of element you want to use. Dealii supports only quads/hexes while fenics focuses on simplex elements ( triangles and tetrahedron). I have found dealii to be quite easy to use once you get past the initial confusion that always occurs with large codes. $\endgroup$
    – BlaB
    Jun 27, 2019 at 10:54
  • $\begingroup$ Hi, we are developing MoFEM; the DG tutorial support mixed meshes with triangles and quads, arbitrary approximation orders. The tutorial example is for 2d but can extend to 3d. mofem.eng.gla.ac.uk/mofem/html/tutorial_dg_poisson.html Also, you can calculate trace skeletons from other spaces, i.e. H1, H-div, and H-curl. For example, to solve the Krochoff plate problem, mofem.eng.gla.ac.uk/mofem/html/tutorial_plate.html Or you can do advection problems, youtu.be/Hz2L4caSAv8 $\endgroup$
    – likask
    Mar 26, 2023 at 11:22

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For Hyperbolic PDEs I can highly recommend Trixi, a (if you want) high order Discontinuous Galerkin based solver with adaptive mesh refining capabilities written in Julia. Both structured and unstructured meshes are supported. Furthermore, the addition of custom initial/boundary conditions, fluxes or entire equations is relatively easy.

Implementing limiters is up to you, but you have access to the basis function coefficients at all times.

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  • $\begingroup$ thanks very much for answering. I had asked this question long back and went ahead with deal.ii. And I don't regret my decision (yet ?) :) $\endgroup$
    – Zxcvasdf
    Oct 26, 2022 at 5:14
  • $\begingroup$ Glad to hear, I just stumbled over the question and wanted to take the possibility to promote Trixi mostly for those, who might come across this question. $\endgroup$
    – Dan Doe
    Oct 26, 2022 at 6:28
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    $\begingroup$ @Zxcvasdf, do you have any specific reasons to use deal.ii in response to your own question? Could be a nice answer to say why you chose it and don't regret choosing it. $\endgroup$
    – user9794
    Nov 24, 2022 at 21:19
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    $\begingroup$ @user9794, I took this decision because of the following: (i) very very well documented code, (ii) availability of plenty of examples/tutorials with detailed explanations, (iii) very active and responsive developer/use group. I cannot compare the technical capabilities because I haven't used other softwares. But the quality and quantity of help available to understand and use the software made me chose this :) $\endgroup$
    – Zxcvasdf
    Mar 28, 2023 at 5:37

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