A simple option could be to define a DG 0 field. Note that:
- it would not be defined only on the boundary, but also in the interior. However, since you never use the value of q in the interior, you could simply leave the values there zero (= the default value)
- it would not be defined only on the centroid of a cell, but in the entire cell, with constant value in the cell. Still, you’d need to extend the values you get from your engineering model anyways, and extending it in a piecewise constant manner is the simplest possible choice.