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

05/28/2020
by   Ruma Rani Maity, et al.
0

The equilibrium configurations of a two dimensional planar bistable nematic liquid crystal device are modelled by a system of second order semi-linear elliptic partial differential equations with non-homogeneous boundary conditions. In this article, Nitsche's method is applied to approximate the solution of this non-linear model. A discrete inf-sup condition sufficient for the stability of a well-posed linear problem is established and this with a fixed point theorem allows the proof of local existence and uniqueness of a discrete solution to the semi-linear problems. A priori and a posteriori energy norm analysis is established for a sufficiently large penalization parameter and sufficiently fine triangulation. Optimal order a priori error estimates in L^2 norm is also established. Several numerical examples that confirm the theoretical results are presented.

READ FULL TEXT

page 20

page 22

page 23

research
07/16/2019

Discontinuous Galerkin Finite Element Methods for the Landau-de Gennes Minimization Problem of Liquid Crystals

We consider a system of second order non-linear elliptic partial differe...
research
11/27/2019

A priori and a posteriori error analysis of an unfitted HDG method for semi-linear elliptic problems

We present a priori and a posteriori error analysis of a high order hybr...
research
01/21/2021

A priori and a posteriori error analysis of the lowest-order NCVEM for second-order linear indefinite elliptic problems

The nonconforming virtual element method (NCVEM) for the approximation o...
research
10/13/2021

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

We analyse an energy minimisation problem recently proposed for modellin...
research
10/29/2021

A Hybrid-High Order Method for Quasilinear Elliptic Problems of Nonmonotone Type

In this paper, we design and analyze a Hybrid-High Order (HHO) approxima...
research
04/01/2020

Bayesian ODE Solvers: The Maximum A Posteriori Estimate

It has recently been established that the numerical solution of ordinary...
research
03/03/2017

Computer-assisted proof of heteroclinic connections in the one-dimensional Ohta-Kawasaki model

We present a computer-assisted proof of heteroclinic connections in the ...

Please sign up or login with your details

Forgot password? Click here to reset