An Adaptive Hierarchical Finite Element Method for Modelling Liquid Crystal Devices

Nematic liquid crystals, hierarchic finite elements, adaptive meshes. Numerical models of liquid crystal devices containing topological defects must take into account two disparate length scales. While the device might extend over several microns, the liquid crystal's alignment varies over nanometres in the region of a defect. Discretising the entire region so finely would be costly in computational terms, but as there are only a few defects, adaptive mesh refinement techniques become attractive. Here, we develop and test an adaptive method which makes use of hierarchical finite elements so that higher order polynomials are used to resolve fine scale features, rather than a finely divided mesh