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We consider polynomial finite elements of order k ≥ 1 for the approximation of Stokes and linear elasticity problems which are continuous in the Gauss-Legendre points of the elements sides, i.e., generalize the Crouzeix-Raviart (k = 1), Fortin-Soulie (k = 2) and Crouzeix-Falk (k = 3) elements. We show that, for odd orders, these Gauss-Legendre elements do not possess a Crouzeix-Velte decomposition...
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