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Example for DG poisson #138
Description
Hi @jorgensd
Are there plans to add a demo for solving the poisson equation using the DG method?
Thanks!
Rem
Hi @jorgensd
Are there plans to add a demo for solving the poisson equation using the DG method?
Thanks!
Rem
Activity
jorgensd commentedon Jul 6, 2023
Hi Rem,
I made a notebook on this a long time ago (main...dokken/dg_tutorial), and it needs some tender love and care to be updated to the main branch, and maybe a review of the mathematics. Maybe @IgorBaratta or @jpdean is willing to help me with this?:)
jpdean commentedon Jul 6, 2023
Sounds good, happy to help. How about DG convection-diffusion though? The convection term doesn't add much difficulty (it's actually easier to understand than the diffusion term), and is often one of the main reasons to use DG. I could update this repo and use it as a starting point. I've also written a tutorial section on DG for convection-diffusion in my thesis which could be used too.
jorgensd commentedon Jul 6, 2023
Fine by me!
RemDelaporteMathurin commentedon Jul 6, 2023
@jorgensd @jpdean Sure a convection diffusion problem would be even more complete!
Let me know if I can give you a hand
My personal agenda is to impose discontinuities at interfaces between materials, maybe one day we'll have a tutorial about this too! 😃
jorgensd commentedon Jul 6, 2023
Hopefully when @jpdean merges his MeshView assembly into DOLFINx.
RemDelaporteMathurin commentedon Jul 6, 2023
I thought we could "just" specify the jump over some internal boundaries? What is MeshView?
jorgensd commentedon Jul 6, 2023
You could, But you would Need to use a DG space for everything. I would like a part mesh Lagrange (continuous) coupled with a continuous solution on another subdomain (with discontinuity between them).
RemDelaporteMathurin commentedon Jul 6, 2023
Oh yes that would be the best!! Please keep me in the loop 🚀
RemDelaporteMathurin commentedon Jul 20, 2023
@jorgensd @jpdean I think I'm almost there with my DG case, just having a hard time finding a tutorial for getting the weak form of the interface condition.
Do you think this is something that could be added to a tutorial too?
jorgensd commentedon Aug 9, 2025
A "pure" DG convection difffusion code could be based of: https://scientificcomputing.github.io/fenics-in-the-wild/src/ucs/uc1_diffusion.html (without time dependency, i.e. https://doi.org/10.1093/imanum/drm050)
and use the analytical solution from section 4.2 of: https://doi.org/10.1137/050634736