An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations

[2304.02062] An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Numerical Analysis arXiv:2304.02062 (math) [Submitted on 4 Apr 2023 ( v1 ), last revised 9 Apr 2026 (this version, v4)] Title: An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations Authors: J.H. Adler , D. B. Emerson View a PDF of the paper titled An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations, by J.H. Adler and D. B. Emerson View PDF HTML (experimental) Abstract: This paper derives an a posteriori error estimator for the nonlinear first-order optimality conditions associated with the electrically and flexoelectrically coupled Frank-Oseen model of liquid crystals, building on previous results for elastic systems. The estimator is proposed for a penalty approach to imposing the unit-length constraint required by the model. Moreover, theory is proven establishing that the estimator provides a reliable estimate of global approximation error and an efficient measure of local error, suitable for use in adaptive refinement. Numerical experiments demonstrate significant improvements in efficiency with adaptive refinement guided by the proposed estimator in a multilevel, nested-iteration framework and superior physical properties for challenging electrically coupled systems. Comments: 18 Pages, 6 Figures. 4 Tables. arXiv admin note: substantial text overlap with arXiv:1806.06248 Subjects: Numerical Analysis (math.NA) MSC classes: 76A15, 65N30, 49M15, 65N22, 65N55 Cite as: arXiv:2304.02062 [math.NA] (or arXiv:2304.02062v4 [math.NA] for this version) https://doi.org/10.48550/arXiv.2304.02062 Focus to learn more arXiv-issued DOI via DataCite Submission history From: David Emerson [ view email ] [v1] Tue, 4 Apr 2023 18:25:25 UTC (1,203 KB) [v2] Mon, 21 Jul 2025 16:00:33 UTC (1,537 KB) [v3] Tue, 13 Jan 2026 14:44:09 UTC (1,532 KB) [v4] Thu, 9 Apr 2026 20:40:21 UTC (1,508 KB) Full-text links: Access Paper: View a PDF of the paper titled An A Posteriori Error Estimator for Electrically Coupled Liquid Crystal Equilibrium Configurations, by J.H. Adler and D. B. Emerson View PDF HTML (experimental) TeX Source view license Current browse context: math.NA < prev | next > new | recent | 2023-04 Change to browse by: cs cs.NA math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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