DG method tutorial

mathematics
1

Hello, everyone. I want to solve a convection-diffusion equations using DG method. Is there any tutorial on how to using DG method in fenics?

2

Going through the usual tutorials page, you’ll find:
https://docs.fenicsproject.org/dolfinx/v0.9.0/python/demos/demo_navier-stokes.html
Although, admittedly, that’s immediately quite advanced.

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3

I have a repository here with a code that solves the time-dependent convection-diffusion equation using a DG scheme with different boundary conditions in FEniCSx. It’s undocumented, but hopefully it might be helpful.

Thanks,

Joe

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4

Dear joe, I really thank for your code. I notice that you use an implicit scheme, but one of my advisors told me that there is no proper implicit numerical scheme for the convection-diffusion equations. Could you give me the full name of the reference where you comment your code on line 94 and 95?

5

I recommend “Mathematical Aspects of Discontinuous Galerkin Methods” by Di Pietro and Ern. They present and analyse DG schemes for the convection-diffusion-reaction equations.

You also might want to check out dolfin_dg, which makes DG schemes easier to implement in FEniCS.

Thanks,

Joe

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