Interest in a step-12-like DG tutorial but for the advection-diffusion equation?

[Bruno Blais]

Dear all,

I hope you are well.

I have been playing with the DG methods within deal.II lately (which has been lots of fun).

I really enjoy the way step-12 is written, especially because of the use of the FEInterfaceValue class. In my opinion it makes low level stuff very easily accessible, yet it is relatively easy to understand.

However, I am under the impression that there are no similar test for elliptic equations in which you need to use Nitsche method + Symmetric Interior Penalty for the boundary + inner faces respectively. I know of step-39, but it does not use the same "low-levelish" features.

I have written such a code for my own pleasure for the laplace equation and I am currently working on its advection-diffusion version (mostly following Larson Chapter 14).

Would it be interesting to turn such a case into a deal.II step (that would follow in step-12 footstep) or does the community feel that the existing steps for DG sufficiently cover the ground?

Best

Bruno

[Timo Heister]

Hi Bruno,

I introduced FEInterfaceValues because I was frustrated by the lack of
DG examples and as a consequence DG users in the community and I
realized that a more intuitive way to teach it was necessary. Of
course we need more than 1 or 2 examples to do that.
I have a lot of unfinished stuff on my machine including working
Laplace and Stokes examples (see my todo list here
https://github.com/dealii/dealii/issues/8884 ) that I haven't gotten
back to yet.

Let me know if you want to work together on something or if you have
any ideas or suggestions.

Best,
Timo

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--
Timo Heister
http://www.math.clemson.edu/~heister/

[Wolfgang Bangerth]

Bruno,

> I really enjoy the way step-12 is written, especially because of the use of
> the FEInterfaceValue class. In my opinion it makes low level stuff very easily
> accessible, yet it is relatively easy to understand.
> However, I am under the impression that there are no similar test for elliptic
> equations in which you need to use Nitsche method + Symmetric Interior Penalty
> for the boundary + inner faces respectively. I know of step-39, but it does
> not use the same "low-levelish" features.

There is also step-47, which probably comes closest to what you're looking for
(even though written for a different equation).

> I have written such a code for my own pleasure for the laplace equation and I
> am currently working on its advection-diffusion version (mostly following
> Larson Chapter 14).
>
> Would it be interesting to turn such a case into a deal.II step (that would
> follow in step-12 footstep) or does the community feel that the existing steps
> for DG sufficiently cover the ground?

Always!
W.

--
------------------------------------------------------------------------
Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/

[Bruno Blais]

Dear Timo,

A step-12-like version of Step-39 for the Laplace equation would be very interesting. I would be glad to help on making one of those. The same could be said about the Stokes equations.

Ideally, once that is done, i would like to try and make one for stabilized Navier-Stokes for both CG and DG, but I feel I need a bit more of experience with writing steps before I move on to that.

So if you feel you need any help with the two aforementioned steps, I would be glad to help. I really like what you have done with the FEInterfaceValues, so if we can make it more popular, why not ? :)!

I am also integrating teaching DG within one of my graduate classes and I feel using deal.II for that will be really helpful.

Best

Bruno

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[luca.heltai]

If you want to take some more inspiration using mesh_loop, ScratchData, and FEInterfaceData, you could take a look at this:

https://github.com/dealii/dealii/blob/master/tests/meshworker/scratch_data_08.cc

where the FEInterfaceValues which is now included in ScratchData is used to solve SIPG on locally refined grids, with just this:



for (unsigned int q = 0; q < p.size(); ++q)
for (unsigned int i = 0; i < n_dofs; ++i)
for (unsigned int j = 0; j < n_dofs; ++j)
{
face_matrix(i, j) +=
(-fev.jump_gradient(i, q) * n[q] * fev.average(j, q) -
fev.average(i, q) * fev.jump_gradient(j, q) * n[q] +
gh * fev.jump(i, q) * fev.jump(j, q)) *
JxW[q];
}
};

:)

Ps: I am planning to extend FEInterfaceValues to be able to extract function values and gradients, so that it can also be used easily with the automatic differentiation tools that
we have, or to easily write a posteriori error estimators… If anybody is looking for a starter project, this may be a very nice one.

L.

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[Timo Heister]

> where the FEInterfaceValues which is now included in ScratchData

Yes, I was going to suggest using that after step-12.

> Ps: I am planning to extend FEInterfaceValues to be able to extract function values and gradients, so that it can also be used easily with the automatic differentiation tools that
> we have, or to easily write a posteriori error estimators… If anybody is looking for a starter project, this may be a very nice one.

Yes, also on my todo list for "some day". :-)