Nitsche method for interface problems

5 months ago by

I want to implement the method in the paper (equation (2.2) and (2.3))
It has the jump in the interface instead of in the facet, and it also need the integration along the interface. I have no idea how to define the second line and the third line in equation (2.3) with ufl form.

Do we have some examples or function to do it?

Community: FEniCS Project
The paper link is timed out. Please add a new link.
written 5 months ago by John Lee  
Hi John,

I've update the paper link. In case the new one is timed out, here is another link. Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems
written 5 months ago by Ting  
I cannot tell from your paper (because I cannot access it) but have you noticed chapter 30 of the FEniCS book, Modeling evolving discontinuities?
written 5 months ago by pf4d  

I did. But these are two different methods. The method in chapter 30 is based on the extended finite element method and I want to implement the Nitsche method.
written 5 months ago by Ting  
Hi, Ting.
I think you need to use the extended FEM technique to have additional DOFs around the interface, and UFL language for bilinear forms are not so different.
I believe the third line of (2.3) is easy using 'jump' command in FEniCS. My only concern is the integration on the interface that the released FEniCS version
probably does not support. You may ask Andre Massing who is working on CutFEM projects with FEniCS. Sorry but this is the best option that I can suggest.
written 5 months ago by John Lee  
Right, the Nitsche method specifies Dirichlet boundary conditions naturally, while the FEniCS implementation of jump integration along interfaces are explained in Ch. 30.
written 5 months ago by pf4d  
Hi, I read the chapter 30 and try to implemented it. But it asked for PUM library which the FEniCS team did not maintain snce 2012?
written 4 months ago by Ting  
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