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The elementary analysis of this paper presents explicit expressions of the constants in the a priori error estimates for the lowest-order Courant, Crouzeix-Raviart nonconforming and Raviart-Thomas mixed finite element methods in the Poisson model problem. The three constants and their dependences on some maximal angle in the triangulation are indeed all comparable and allow accurate a priori error control.doi:10.4208/jcm.1108-m3677 fatcat:7ghjarh54vfutje7qex7ver5vi