  We present a robust discretization of the Ericksen model of liquid crystals
with variable degree of orientation coupled with colloidal effects and electric
fields. The total energy consists of the Ericksen energy, a weak anchoring (or
penalized Dirichlet) energy to model colloids, and an electrical energy for a
given electric field. We describe our special discretization of the total
energy along with a method to compute minimizers via a discrete quasi-gradient
flow algorithm which has a strictly monotone energy decreasing property.
Numerical experiments are given in two and three dimensions to illustrate that
the method is able to capture non-trivial defect patterns, such as the Saturn
ring defect. We conclude with a rigorous proof of the Gamma-convergence of our
discrete energy to the continuous energy.
