Tensor finite elements for smectic liquid crystals
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909624081317888 |
|---|---|
| author | Führer, Thomas Heuer, Norbert Linß, Torsten |
| author_facet | Führer, Thomas Heuer, Norbert Linß, Torsten |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor finite elements for smectic liquid crystals Führer, Thomas Heuer, Norbert Linß, Torsten Numerical Analysis 65N30, 76A15, 49J10, 35B45, 65N12 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. |
| title | Tensor finite elements for smectic liquid crystals |
| topic | Numerical Analysis 65N30, 76A15, 49J10, 35B45, 65N12 |
| url | https://arxiv.org/abs/2505.20493 |