Midpoint of edge line implemented in fenics

Hi everyone, I have a exterior boundary equation to implement in Fenics.This equation is listed below, where Hz1, Hz2 and psi are defined at the two ends of edge lines, the right hand of the equation is defined at the edge center which is a known function. How to implement this equation in Fenics? Thank you in advance!

Peruse the periodic table of finite elements and select that which suits your regularity requirements.

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Dear nate, thanks for your reply. My problem is a finite element boundary integration type(FE-BI) which is used to truncate the unlimited space. In the domain the usual node basis functions are used, while on the boundary of the truncated domain the constant value pulse functions are used at the center of every edge. The solution expanded with these pulse functions is the average of the solutions at the two end nodes of the boundary edges. It may be not a problem with only one kind of finite element in the periodic table to be solved.

Indeed, so don’t restrict yourself to one kind of finite element.

Dear nate, in order to make myself clearer, I list the weak form to be implemented in Fenics. The 3rd term on the left hand is the boundary integration. The pulse function P is defined on the boundary edge. Ni and Nj are the node basis functions.