Hi @Jeremy_Bleyer and FeniCS support team,
Greetings!
I have gone through biharmonic example for implementing C1 continuity using DG functionspace method of jump and averages. I have a general query related to my implementation,
If my bilinear form contains multiple terms of first derivatives (requiring C1 continuity) like
a(w, v) = \int_{\Omega} \sum_{i=1}^{N} \frac{d w}{d x} \cdot f_i(x_2, x_3) \, v \, dx. To implement continuity constraint of first derivatives, does the below updated bilinear form works,
\begin{align}
a(w, v) = &\int_{\Omega} \sum_{i=1}^{N} \frac{d w}{d x} \cdot f_i(x_2, x_3) \, v \, dx \\
&- \int_{E} \left\langle \frac{d w}{d x} \right\rangle \, [\![ v ]\!] \, ds \\
&- \int_{E} [\![ w ]\!] \, \left\langle \frac{d v}{d x} \right\rangle \, ds \\
&+ \alpha \int_{E} \frac{1}{h_E} [\![ w ]\!] \, [\![ v ]\!] \, ds.
\end{align}
Meaning, do we need to apply a pair of jump and average for first derivative only once, or option b, for all 5 first derivatives terms separately in my original weak form.
Any help or reference is greatly appreciated.