Tensor finite elements for smectic liquid crystals
Numerical Analysis
2025-05-28 v1 Numerical Analysis
Abstract
We present a tensor-based finite element scheme for a smectic-A liquid crystal model. We propose a simple C\'ea-type finite element projection in the linear case and prove its quasi-optimal convergence. Special emphasis is put on the formulation and treatment of appropriate boundary conditions. For the nonlinear case we present a formulation in two space dimensions and prove the existence of a solution. We propose a discretization that extends the linear case in Uzawa-fashion to the nonlinear case by an additional Poisson solver. Numerical results illustrate the performance and convergence of our schemes.
Cite
@article{arxiv.2505.20493,
title = {Tensor finite elements for smectic liquid crystals},
author = {Thomas Führer and Norbert Heuer and Torsten Linß},
journal= {arXiv preprint arXiv:2505.20493},
year = {2025}
}