Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model Article Swipe
Ricardo H. Nochetto
,
Michele Ruggeri
,
Shuo Yang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/21m1407495
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.1137/21m1407495
The Ericksen model for nematic liquid crystals couples a director field with a scalar degree of orientation variable and allows the formation of various defects with finite energy. We propose a simple but novel finite element approximation of the problem that can be implemented easily within standard finite element packages. Our scheme is projection-free and thus circumvents the use of weakly acute meshes, which are quite restrictive in three dimensions but are required by recent algorithms for convergence. We prove stability and $\Gamma$-convergence properties of the new method in the presence of defects. We also design an effective nested gradient flow algorithm for computing minimizers that controls the violation of the unit-length constraint of the director. We present several simulations in two and three dimensions that document the performance of the proposed scheme and its ability to capture quite intriguing defects.
Related Topics
Concepts
Finite element method
Mathematics
Polygon mesh
Liquid crystal
Convergence (economics)
Projection (relational algebra)
Mathematical analysis
Scalar (mathematics)
Constraint (computer-aided design)
Scalar field
Applied mathematics
Geometry
Algorithm
Physics
Mathematical physics
Optics
Economic growth
Thermodynamics
Economics
Metadata
- Type
- article
- Language
- en
- Landing Page
- https://doi.org/10.1137/21m1407495
- OA Status
- green
- Cited By
- 2
- References
- 28
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W3138374136
All OpenAlex metadata
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https://openalex.org/W3138374136Canonical identifier for this work in OpenAlex
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https://doi.org/10.1137/21m1407495Digital Object Identifier
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Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen ModelWork title
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articleOpenAlex work type
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enPrimary language
- Publication year
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2022Year of publication
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2022-04-01Full publication date if available
- Authors
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Ricardo H. Nochetto, Michele Ruggeri, Shuo YangList of authors in order
- Landing page
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https://doi.org/10.1137/21m1407495Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
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https://hdl.handle.net/11585/944078Direct OA link when available
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Finite element method, Mathematics, Polygon mesh, Liquid crystal, Convergence (economics), Projection (relational algebra), Mathematical analysis, Scalar (mathematics), Constraint (computer-aided design), Scalar field, Applied mathematics, Geometry, Algorithm, Physics, Mathematical physics, Optics, Economic growth, Thermodynamics, EconomicsTop concepts (fields/topics) attached by OpenAlex
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2Total citation count in OpenAlex
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2025: 1, 2023: 1Per-year citation counts (last 5 years)
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10Other works algorithmically related by OpenAlex
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