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And this is where I'm having troubles. The weak form of the problem when dealing with discontinuous Galerkin elements (the usual weak form can be found by taking the divergence of the PDE, multiplying it by a test function ##v## and integrating it over the whole domain, applying integration by parts) is apparently very complicated compared to the case where the elements are continuous. For example, the lines 86 to 93 of https://bitbucket.org/fenics-projec...mo/undocumented/dg-poisson/demo_dg-poisson.py show such an example. There are terms from Nitsche that apply to the boundaries where Dirichlet conditions are present, and other terms applied on the interface between the materials where the discontinuity is imposed. But I do not quite understand all of it, and I am not sure how to apply this to my equation.

I have tried to follow the tutorial at https://github.com/jorgensd/dolfinx-tutorial/blob/dokken/dg_tutorial/chapter1/dg.ipynb, but I am still unsure on how to apply it to my equation. If someone could guide me on how to find the expression for the weak form, I'd be happy.