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The authors analyze high-frequency electromagnetic and acoustic scattering problems by the finite element coupled to Pade-type absorbing boundary conditions (ABCs). These new ABCs are local and can furthermore be applied on arbitrarily convex-shaped boundaries. The accuracy of the proposed method is investigated through different model problems. The obtained results show that relatively small computational domain can be considered in comparison with the classical second-order Bayliss- Gunzburger-Turkel ABCs while yielding accurate computations.