“…grid R ε , each cell of the grid having the size ∼ ε β with β ∈ (0, 1) (i.e., much larger than the length-scale of a vortex) such that the energy E ε (u ε ; R ε ) on the 1-dimensional grid R ε is of order E ε (u ε ; Ω)/ε β . Then Theorem 1 implies that |u ε | − 1 behaves as a positive power of ε in Ω, and v ε = u ε /|u ε | is a "good" approximation of u ε (in terms of the L 2 norm, their global Jacobian etc., see [8]). In that context, we give the following consequence of Theorem 1 for a cell of the grid leading to a key estimate needed in [8] (only a weaker version of this key estimate was needed in [9,5]):…”