Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics

Mouhamadou Samsidy Goudiaby; Ababacar Diagne; Leon Matar Tine

doi:10.3934/cpaa.2021116

Article Contents

2021, Volume 20, Issue 10: 3499-3514. Doi: 10.3934/cpaa.2021116 open access

This issue Previous Article A new Carleson measure adapted to multi-level ellipsoid covers Next Article Regular attractors of asymptotically autonomous stochastic 3D Brinkman-Forchheimer equations with delays

Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics

1.
Département de mathématiques, UFR des Sciences et Technologies, Université Assane Seck, BP 523 Ziguinchor, Sénégal
2.
Svenska Handelsbanken, Capital Market, Blasieholmstorg 11,106 70 STOCKHOLM, Sweden
3.
Institut Camille Jordan, Université Claude Bernard Lyon 1, Avenue Claude Bernard 69622 VILLEURBANNE cedex, France

^* Corresponding author
^* Corresponding author

Received: March 2021

Revised: June 2021

Early access: July 2021

Published: October 2021

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Abstract

We consider an unconditional fully discrete finite element scheme for a nematic liquid crystal flow with different kinematic transport properties. We prove that the scheme converges towards a unique critical point of the elastic energy subject to the finite element subspace, when the number of time steps go to infinity while the time step and mesh size are fixed. A Lojasiewicz type inequality, which is the key for getting the time asymptotic convergence of the whole sequence furnished by the numerical scheme, is also derived.

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Mathematics Subject Classification: 35Q35, 35K55, 35B40, 65M60.

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References

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