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arXiv · 2512.24928

A finite element approach for minimizing line and surface energies arising in the study of singularities in liquid crystals

Dominik Stantejsky
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Abstract

Motivated by a problem originating in the study of defect structures in nematic liquid crystals, we describe and study a numerical algorithm for the resolution of a Plateau-like problem. The energy contains the area of a two-dimensional surface $T$ and the length of its boundary $\partial T$ reduced by a prescribed curve to make our problem non-trivial. We additionally include an obstacle $E$ for $T$ and pose a surface energy on $E$. We present an algorithm based on the Alternating Direction Method of Multipliers that minimizes a discretized version of the energy using finite elements, generalizing existing TV-minimization methods. We study different inclusion shapes demonstrating the rich structure of minimizing configurations and provide physical interpretation of our findings for colloidal particles in nematic liquid crystal.

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Dominik Stantejsky. 2025-12-31. A finite element approach for minimizing line and surface energies arising in the study of singularities in liquid crystals. https://arxiv.org/abs/2512.24928

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