I am relatively new to both FEniCS and finite elements and Galerkin methods so I apologize for if this question is a little too basic.
I want to solve the Poisson equation for pressure in a rectangular domain with a fracture inside. This fracture means that I have an interior boundary across which the solution will jump (i.e. I expect my solution to be discontinuous across the interior boundary). Does this mean that I need to solve the equation using discontinuous Galerkin (DG) as opposed to the simpler "CG" method?
I have looked through questions on this forum and online in general but I haven't found any examples of people solving problems in FEniCS with discontinuous solutions but I'm sure they are out there. Any links to relevant examples would also be greatly appreciated.
Thanks!
edit: I would like to add that the fracture does not split the domain into two separate parts. To be more specific, my domain is just a unit square for now and the fracture (interior boundary) will be at x[0]=0.5 and 0.25<x[1]<0.75. I found another question which is very similar to mine and I link to below, but I feel that mine is a bit different because there aren't two distinct subdomains.
https://fenicsproject.org/qa/10927/neumann-bc-depending-on-solution?show=10927#q10927
