Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model

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