Integral on only intefaces, not on boundary faces

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1

I tried to implement DG method for the following problem: Find (u_h,p_h)such that [tex]a_h(u_h, v_h) + b_h(v_h, p_h)-b_h(u_h, q_h)+ s_h(p_h, q_h)=\int_\Omega f\cdot v_h,\forall v_h \in U_h, \forall q_h \in P_h,[/tex]
where [tex]s_h(q_h, r_h):=\sum\limits_{F\in \mathcal{F}^i_h}h_F\int_F[[q_h]][[r_h]].[/tex]
I used sh*dx(skeleton=True) as in the tutorial to compute the integral on inteface of s_h, but there is a traceback call.

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I also attached my .ipynb file. Could you please show me fixed this error or how to compute that integral on only interfaces?
Thank you so much.

Attachment: Capture3.JPG

Attachment: fem1.ipynb

2

Hi dong,

you need to set the dgjumps flag for a DG formulation as described here

V = VectorH1(mesh,order=2, dirichlet ='left|right|top|bottom', dgjumps=True) Q = H1(mesh,order=1) X = FESpace([V,Q], dgjumps=True)

Then your code should run through.

Best
Michael

3

Thank you for your help. The code run smoothly now.