Andreas Prohl

Calderer

Elliott

Ericksen

Existence

John W. Barrett

Meyers

Xiaobing Feng

ESAIM Mathematical Modelling and Numerical Analysis

English

Barrett, John W.

Feng, Xiaobing

Prohl, Andreas

Numérisation de Documents Anciens Mathématiques

Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation

Crossref

We consider a degenerate parabolic system which models
the evolution of nematic liquid crystal with variable degree of orientation.
The system
is a slight modification
to that proposed in [Calderer et al., SIAM J. Math. Anal. 33 (2002) 1033–1047], which is a special case of 
Ericksen's general continuum model in [Ericksen, Arch. Ration. Mech. Anal. 113 (1991) 97–120]. 
We prove the global existence 
of weak solutions by passing to the limit in a regularized system. 
Moreover, we 
propose a practical fully discrete finite element method for this 
regularized 
system, and we establish the (subsequence) convergence 
of this finite element approximation 
to the 
solution of the regularized system as the mesh parameters tend to zero; and
to a solution of the original degenerate parabolic system 
when the 
the mesh and regularization parameters 
all approach zero. 
Finally, numerical experiments are included 
which show the 
formation, annihilation and evolution of line singularities/defects 
in such models

EDP Sciences OAI-PMH repository (1.2.0)

Convergence of a fully discrete finite element method 
 for a degenerate parabolic system modelling nematic liquid crystals 
with
variable degree of orientation

Barrett, JW

Feng, XB

Prohl, A

Spiral - Imperial College Digital Repository

A ﬁnite element model for the time-dependent joule heating problem.

An Lp estimate for the gradient of solutions of second order elliptic divergence equations.

Existence for a model arising from the in situ vitriﬁcation process.

Liquid crystals with variable degree of orientation.

Nonlinear Functional Analysis and Its Applications,

Numerical Methods for Nonlinear Variational Problems.

Sobolev Spaces.

Time evolution of nematic liquid crystals with variable degree of orientation.

http://www.esaim-m2an.org/articles/m2an/pdf/2006/01/m2an0513.pdf

Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation

Abstract

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Numérisation de Documents Anciens Mathématiques

Crossref

EDP Sciences OAI-PMH repository (1.2.0)

Spiral - Imperial College Digital Repository

Crossref