# C1 continuity functions available for quad and interval mesh\_dolfinx?

**URL:** <https://fenicsproject.discourse.group/t/c1-continuity-functions-available-for-quad-and-interval-mesh-dolfinx/16109>\
**Category:** dolfinx\
**Created:** [October 24, 2024, 5:23pm UTC](https://fenicsproject.discourse.group/t/c1-continuity-functions-available-for-quad-and-interval-mesh-dolfinx/16109 "2024-10-24T17:23:11Z")\
**Posts on this page:** 1\
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**Author:** ![bagla0](https://yyz2.discourse-cdn.com/free1/user_avatar/fenicsproject.discourse.group/bagla0/32/4677_2.png) [@bagla0](https://fenicsproject.discourse.group/u/bagla0)\
**Post date:** [October 27, 2024, 11:07pm UTC](https://fenicsproject.discourse.group/t/c1-continuity-functions-available-for-quad-and-interval-mesh-dolfinx/16109/5 "2024-10-27T23:07:09Z")

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Hi @Jeremy_Bleyer and FeniCS support team,

Greetings!

I have gone through [biharmonic example](https://fenics.readthedocs.io/projects/dolfin/en/2017.2.0/demos/biharmonic/python/demo_biharmonic.py.html) 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.

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