  We design a finite element method (FEM) for a membrane model of liquid
crystal polymer networks (LCNs). This model consists of a minimization problem
of a non-convex stretching energy. We discuss properties of this energy
functional such as lack of weak lower semicontinuity. We devise a
discretization with regularization, propose a novel iterative scheme to solve
the non-convex discrete minimization problem, and prove stability of the scheme
and convergence of discrete minimizers. We present numerical simulations to
illustrate convergence properties of our algorithm and features of the model.
