A structure-preserving FEM for the uniaxially constrained \(\mathbf{Q} \)-tensor model of nematic liquid crystals

DOI10.1007/s00211-020-01133-zzbMath1446.65160arXiv1911.04347OpenAlexW3042898385MaRDI QIDQ2194043

Ricardo H. Nochetto, Shawn W. Walker, Juan Pablo Borthagaray

Publication date: 25 August 2020

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.04347

zbMATH Keywords

finite element methoddefectsgamma-convergenceLandau-de Gennesliquid crystals

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) PDEs in connection with fluid mechanics (35Q35) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Degenerate elliptic equations (35J70) Liquid crystals (76A15) Integro-partial differential equations (35R09) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (10)

Accelerated Gradient Descent Methods for the Uniaxially Constrained Landau-de Gennes Model ⋮ Parameter dependent finite element analysis for ferronematics solutions ⋮ Modelling and computation of liquid crystals ⋮ Numerical method for the equilibrium configurations of a Maier-Saupe bulk potential in a Q-tensor model of an anisotropic nematic liquid crystal ⋮ Gamma-Convergent Projection-Free Finite Element Methods for Nematic Liquid Crystals: The Ericksen Model ⋮ Variational and numerical analysis of aQ-tensor model for smectic-A liquid crystals ⋮ Optimal Control of the Landau–de Gennes Model of Nematic Liquid Crystals ⋮ Quasi-Optimal Error Estimates for the Finite Element Approximation of Stable Harmonic Maps with Nodal Constraints ⋮ On the convergence of an IEQ-based first-order semi-discrete scheme for the Beris-Edwards system ⋮ The Q-tensor model with uniaxial constraint

Uses Software

• FELICITY

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Semi-discrete energy-stable schemes for a tensor-based hydrodynamic model of nematic liquid crystal flows
• Numerical solution of the Ericksen-Leslie dynamic equations for two-dimensional nematic liquid crystal flows
• Local minimization, variational evolution and \(\Gamma\)-convergence
• Orientability and energy minimization in liquid crystal models
• A mesh adaptivity scheme on the Landau-de Gennes functional minimization case in 3D, and its driving efficiency
• Existence of minimal energy configurations of nematic liquid crystals with variable degree of orientation
• Liquid crystals with variable degree of orientation
• An introduction to \(\Gamma\)-convergence
• The Ericksen model of liquid crystals with colloidal and electric effects
• A decoupled energy stable scheme for a hydrodynamic phase-field model of mixtures of nematic liquid crystals and viscous fluids
• Maximum principle and uniform convergence for the finite element method
• Numerical approximation of nematic liquid crystal flows governed by the Ericksen-Leslie equations
• Dissipative Ordered Fluids
• A Renormalized Newton Method for Liquid Crystal Director Modeling
• Simulation of Q-Tensor Fields with Constant Orientational Order Parameter in the Theory of Uniaxial Nematic Liquid Crystals
• A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
• An Energy-Minimization Finite-Element Approach for the Frank--Oseen Model of Nematic Liquid Crystals
• On nematic liquid crystals with variable degree of orientation
• Equilibrium order parameters of nematic liquid crystals in the Landau-de Gennes theory
• An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
• Numerical analysis of a finite element scheme for the approximation of harmonic maps into surfaces
• Local minimisers and singular perturbations
• Relaxation Methods for Liquid Crystal Problems
• A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case
• Finite Element Analysis of the Landau--de Gennes Minimization Problem for Liquid Crystals
• FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling
• Mathematical Modeling in Continuum Mechanics
• Approximation of Liquid Crystal Flows
• SCALINGS AND LIMITS OF LANDAU-DE GENNES MODELS FOR LIQUID CRYSTALS: A COMMENT ON SOME RECENT ANALYTICAL PAPERS
• A Finite Element Method for Nematic Liquid Crystals with Variable Degree of Orientation
• A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model
• Convergence rates of symplectic Pontryagin approximations in optimal control theory
• On Lipschitz analysis and Lipschitz synthesis for the phase retrieval problem

This page was built for publication: A structure-preserving FEM for the uniaxially constrained \(\mathbf{Q} \)-tensor model of nematic liquid crystals