As expected, for a given number of DOF a more accurate solution can be achieved by adaptive, local h-refinement, as compared to global refinement in a fully matching setting.
This is easily guaranteed, if we start from a fully matching setting, apply substructuring by cross-insertion as described in Section 5.2, and select primal DOF at all subdomain vertices which are not hanging.
Note that the generalization of (12) given in (16) might seem superfluous in the fully matching setting, but it will be needed in Section 5 in the context of cases which are not fully matching.
If we start from a fully matching setting, apply 1-level substructuring by cross-insertion, and choose all non-hanging vertices as primal vertices, then it is guaranteed that there are at least two primal vertices, i.e., at least four primal DOF, on each subdomain.
Condition (ii) for the fully matching setting implies that each DOF u k (i ), k ∈ B (i, j ), can be identified with a DOF u ℓ (j ), ℓ ∈ B (j, i ), such that the corresponding basis functions match as in (12).
In an alias matching setting (described in more detail in [9]), we cannot assume that we have knowledge of all potential authors.
