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.

  • 1
    $\begingroup$ 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
    Commented 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
    Commented 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
    Commented Mar 26, 2023 at 11:22

1 Answer 1


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.

  • $\begingroup$ 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
    Commented 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
    Commented Oct 26, 2022 at 6:28
  • 2
    $\begingroup$ @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
    Commented Nov 24, 2022 at 21:19
  • 2
    $\begingroup$ @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
    Commented Mar 28, 2023 at 5:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.