In this work we will present a new 3-D full-wave finite element formulation and its application to the numerical modelling of high temperature superconductors. This new approach has the electric field as the main unknown, which allows the direct calculation of the induced eddy currents and other magnitudes of interest (e.g. Joule heating) without resorting to derivatives. It does not require the addition of extra unknowns (e.g Lagrange multipliers or scalar potentials) to be stable and it can account for capacitive and inductive effects simultaneously, even at low frequencies. The new approach applies mass-lumping L2 projections on the curl and divergence operators of the regularized Maxwell equations weak form and uses first order Lagrangian nodal finite elements enriched with an inner bubble. In this work we will also explore the possibility of converting the time-dependent non-linear problem in several parallel non-linear problems in frequency domain, which can be solved independently (avoiding sequential time-stepping) with the consequent savings of computational costs.