In the scope of finite element methods, the interpolation of solutions in a space of piecewise polynomial functions present spatial oscillations when solutions with discontinuities or high gradients are sought. Euler equations of gas dynamics modelled with discontinuous Galerkin methods also present such oscillations when shocks are captured within continuous portions of the domain. To stabilize these oscillations in such a scheme, artificial diffusive terms are added to the formulation. Several artificial diffusive terms are documented in the bibliography, but their implementations remain challenging. The authors document the development of the 2D and 3D artificial diffusive terms of Least Squares, SUPG and Bornhaus in an object oriented framework. The SUPG and BORNHAUS terms require a matricial decomposition which has been implemented in the symbolic mathematical software (Mathematica).