How to calculate the error on the skeleton of mesh

#mesh
from netgen.geom2d import SplineGeometry
geo = SplineGeometry()
geo.AddRectangle( (0, 0), (1, 1))
mesh = Mesh( geo.GenerateMesh(maxh=1/16))
#
velocity = CoefficientFunction(UN.components[0:2])
err_u = sqrt (Integrate ( (velocity-exact_u)*(velocity-exact_u), mesh))
#
Now，I want to calculate the error on the skeleton of mesh， namely ，the L^2 error of mass flux jump [v_h] \cdot n
#tex
[tex] \sum_{F \in \mathcal{F}_{h}} \frac{1}{h_{F}}\left\| \llbracket {v}_{h} \rrbracket \cdot {n}_{F}\|_{L^{2}(F)}^{2}[/tex]
#\mathcal{F}_{h} stand for all facets of mesh

Hi Yongbin,

The simplest way to compute this quantity is by defining a bilinear form a so that a(u,u) coincides with your (sum of) integral(s). Then you Apply the bilinear form to your discrete solution u and take the inner product of the result with u again.

Best,
Christoph

Hi，Christoph，

Thank you very much for your reply. Sorry，I may not fully understand what you mean. This is my code for Stokes . I don't know how to calculate in my code. In addition，I also wonder， is there other way to calculate？

Thank you again！

Yongbin

Hi Yongbin,

Here is the code fitting your script. I use hybrid dg jumps here as you use a hybrid DG formulation: Alternatively, if you are interested in the standard DG jumps the code looks as follows: Alternatives? I think this is the most straight-forward way to do it. As of now there is no "Integrate" equivalent that would allow you to integrate the skeleton-terms directly. However, I think the above approach is also very natural.

Best,
Christoph

I have successfully solved this problem according to your reply, thank you very much for your reply!



Yongbin Han

Hi Yongbin,

often one needs these terms in residual-type error estimators. Then you need them element by element.

This is now also supported:
full example is attached.

You can integrate elementwise, on every element boundary, and use also values from the neighbouring elements.

This is a quite new feature and needs some more testing. Faces at the domain boundary are skipped, at the moment.

Joachim