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=== Compactness (needed for some nonlinear problems)===
For all sequence <math>(u_m)_{m\in\mathbb{N}}</math> such that <math>u_m \in X_{D_m,0} </math> for all <math>m\in\mathbb{N}</math> and <math>(\Vert u_m\Vert_{D_m})_{m\in\mathbb{N}}</math> is bounded, then the sequence <math>(\Pi_{D_m} u_m)_{m\in\mathbb{N}}</math> is relatively compact in <math>L^2(\Omega)</math> (this property implies the coercivity property).
=== Piecewise constant reconstruction (needed for some nonlinear problems)===
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