  The Ericksen model for nematic liquid crystals couples a director field with
a scalar degree of orientation variable, and allows the formation of various
defects with finite energy. We propose a simple but novel finite element
approximation of the problem that can be implemented easily within standard
finite element packages. Our scheme is projection-free and thus circumvents the
use of weakly acute meshes, which are quite restrictive in 3D but are required
by recent algorithms for convergence. We prove stability and
$\Gamma$-convergence properties of the new method in the presence of defects.
We also design an effective nested gradient flow algorithm for computing
minimizers that controls the violation of the unit-length constraint of the
director. We present several simulations in 2D and 3D that document the
performance of the proposed scheme and its ability to capture quite intriguing
defects.
