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A discontinuous finite element formulation for Helmholtz problems is presented with C⁰ continuity across inter-element boundaries enforced in a weak sense depending on two parameters β and λ whose choice is crucial for the performance of the proposed method. These parameters are chosen through one dimension numerical experiments aiming at minimizing the pollution error. Optimal values of these parameters are then adopted in more general situations. The accuracy and stability of the proposed formulation for linear and bilinear shape functions are demonstrated in several numerical examples in one and two dimensions.