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Journal Articles Communications on Pure and Applied Analysis Year : 2021

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

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.

Dates and versions

hal-03534380 , version 1 (19-01-2022)

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Cite

Mouhamadou Samsidy Goudiaby, Ababacar Diagne, Léon Matar Tine. Longtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics. Communications on Pure and Applied Analysis, 2021, 20 (10), pp.1-16. ⟨10.3934/cpaa.2021116⟩. ⟨hal-03534380⟩
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