Tensor finite elements for smectic liquid crystals
Abstract
We present a tensor-based finite element scheme for a smectic-A liquid crystal model. We propose a simple Céa-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.
Fields of Study & Subjects
Liquid Crystal Research Advancements
Mathematics and Applications
Advanced Materials and Mechanics
Publication details
- Journal / source
- Mathematical Models and Methods in Applied Sciences
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 36
- Issue
- 12
- Pages
- 2817–2843
- Publication date
- 9 June 2026
- Language
- EN