There is growing interest in superconducting machinery design in AC regime such as generators, motors, and magnets. High-temperature superconductors are used as tapes or cables for the machine windings. Therefore, AC losses have to be evaluated efficiently for an optimal design. Moreover, non-linearities, arising from the power law characterizing the electrical behaviour of superconductor, have to be also dealt with. The development of efficient numerical methods is therefore critical to model high-temperature superconductors. Although numerous methods have already been proposed, the finite element method applied on the time-dependent curl-curl–based H-formulation remains the mostly used. It uses edge elements of Nedelec to naturally ensure the continuity of the tangential components of H. To take into account non-linearities from superconductors, a linearisation of the superconductors constitutive power law E=ρ(J)J was implemented. Discontinuous Galerkin finite element method provides an interesting alternative to edge elements for the time-dependent H-formulation. Indeed, the curl-curl operator is written as a div operator and the interior penalty approach defines numerical fluxes at the interfaces. Those fluxes will ensure the continuity of the tangential components of H. The resistivity ρ(J) is explicitly evaluated at the previous iteration with such an approach leading to convergence. In this paper, both numerical approaches implementation will be presented. We will also compare the numerical results from those methods applied to 3D modelling of simple superconducting geometries in AC regime.