Something like this[1]? There are discontinuous elements
This is a first google hit,
https://community.freefem.org/t/problem-in-3d-discontinuous-galerkin-computation/2015/5
I’ve never used these but curious, If you can post a worked example with
solution I can try to do it in FF if I get a chance.
[1]A modified weak Galerkin finite element method for the Stokes equations, Mu , Lin[ ...] Ye , Xiu; Journal of Computational and Applied Mathematics. 2015
https://www.sciencedirect.com/science/article/pii/S037704271400363X