  We study the Landau-de Gennes Q-tensor model of liquid crystals subjected to
an electric field and develop a fully discrete numerical scheme for its
solution. The scheme uses a convex splitting of the bulk potential, and we
introduce a truncation operator for the Q-tensors to ensure well-posedness of
the problem. We prove the stability and well-posedness of the scheme. Finally,
making a restriction on the admissible parameters of the scheme, we show that
up to a subsequence, solutions to the fully discrete scheme converge to weak
solutions of the Q-tensor model as the time step and mesh are refined. We then
present numerical results computed by the numerical scheme, among which, we
show that it is possible to simulate the Fr\'eedericksz transition with this
scheme.
