I am thinking to use discontinuous galerkin FEM (DGFEM) method to estimate discontinuous displacement field $u: \Omega \rightarrow \mathbb{R}^2$ at the crack surface of a material.
The domain is discretized with triangles. I can think two ways to define control points where we evaluate displacement fields
- Control points are defined on vertices/nodes of a triangle (probably knows as nodal DGFEM in the literature)
- Control points are defined on mid-points of the edges. (like in Crouzeix–Raviart elements)
I could not find a reference where second method has been employed to model DGFEM.
Will there be something wrong mathematically if we define control points on mid-points of edges to model DGEM?