Hi all, This is a simpler version of the problem stated in Imposing a discontinuity in the solution, on an internal interface I’d like (in dolfinx) to impose a discontinuity at the interface between two domains. I understood that MeshView would be the best option since we would have CG elements e…

Such discontinuities occur for instance in the case of a thermal contact resistance (temperature jump) or conservation of chemical potential for mass transport (jump in concentration)

Fair enough. I must read more on the other uses of the Poisson equation :slight_smile:

Thanks for this. I read through section 3 but I’m afraid my poor mathematical background is too light to understand a substantial fraction of this… I’ll carry on looking for a demo :slight_smile:

This is the updated code for dolfinx 0.7.0 from dolfinx import mesh, fem, plot import dolfinx.fem.petsc import dolfinx.nls.petsc from mpi4py import MPI import ufl from petsc4py import PETSc from ufl import dx, grad, dot, jump, avg import numpy as np msh = mesh.create_unit_square(MPI.COMM_WORLD, 8,…

Does it work exactly as intended? I’m asking because I’m still very interested in this (I am the asker in your link of your 1st post), and I got stuck.

It’s not working at the minute and I must admit we are all banging our head against the wall with this because the maths aren’t trivial and we are not maths people :joy:

I see… This shouldn’t be rocket science. Physically, it is very simple, there’s a discontinuity in the voltage or temperature (a scalar field), that is proportional to a resistance (electrical or thermal in those 2 cases). Extremely simple mathematically. This is implemented in COMSOL and in a myri…

I am also interested in how to code this in dolfinx. In my problem, I have a discontinuity in the field at the internal boundary with the flux proportional to the jump in the field: \nabla u \cdot \hat{\mathbf{n}} = \alpha (u_{+} - u_{-}) where \alpha \in \mathbb{R} I also used the DG formulation …

Isn’t there a jump missing in the boundary condition here? What side is the [image] leshinka: ∇u⋅^n Evaluated at? This is a discontinuous quantity, and the normal is pointing in different directions depending on what cell you are in.

I have \nabla u \cdot \hat{n}(+) = \alpha (u_{+} - u_{-}) and because the flux is continuous, then I also have \nabla u \cdot \hat{n}(-) = \alpha (u_{-} - u_{+})

Imposing a discontinuity at interface using DG method

dolfinx

dokken January 18, 2024, 6:10pm 27

See Issues visualizing multiple fields stored in single XDMF file [dolfinx] - #5 by dokken

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Imposing a discontinuity at interface using DG method

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