Create a finite element space with coupled boundary condition


I want to create the following finite element space on [0,1]^2: on every triangle I want continuous piecewise quadratics X RT_2, with the condition that for (eta,v) in this space we have v \cdot n - i eta=0 on the boundary of the domain (here n is the normal vector of the boundary, and i^2=-1).

Note that the normal component of RT_2 functions are in fact quadratic functions.

Is there an easy way of making this space?

Best regards,

do you accept to use a Lagrange multiplier to enforce that constraint ?

Thanks for the quick reply! This seems like an interesting idea, but we are not sure if we can rewrite our problem using a Lagrangian, we will try. I presume making this space explicitly is difficult?