Variational and numerical analysis of a 𝐐-tensor model for smectic-A liquid crystals

10/13/2021
by   Jingmin Xia, et al.
0

We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the tensor-valued nematic order parameter 𝐐 and a fourth-order equation for the scalar-valued smectic density variation u. Our two main results are a proof of the existence of solutions to the minimisation problem, and the derivation of a priori error estimates for its discretisation using the 𝒞^0 interior penalty method. More specifically, optimal rates in the H^1 and L^2 norms are obtained for 𝐐, while optimal rates in a mesh-dependent norm and L^2 norm are obtained for u. Numerical experiments confirm the rates of convergence.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

12/21/2020

Existence results and iterative method for solving a fourth order nonlinear integro-differential equation

In this paper we consider a class of fourth order nonlinear integro-diff...
02/05/2021

Singular perturbation results for linear partial differential-algebraic equations of hyperbolic type

We consider constrained partial differential equations of hyperbolic typ...
05/28/2020

A priori and a posteriori error analysis for the Nitsche's method of a reduced Landau-de Gennes problem

The equilibrium configurations of a two dimensional planar bistable nema...
06/22/2020

A second order accurate numerical scheme for the porous medium equation by an energetic variational approach

The porous medium equation (PME) is a typical nonlinear degenerate parab...
10/09/2019

Convergence analysis of a numerical scheme for the porous medium equation by an energetic variational approach

The porous medium equation (PME) is a typical nonlinear degenerate parab...
10/28/2019

A framework for second order eigenvector centralities and clustering coefficients

We propose and analyse a general tensor-based framework for incorporatin...
10/20/2021

A C^0 interior penalty method for mth-Laplace equation

In this paper, we propose a C^0 interior penalty method for mth-Laplace ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.