Open AccessLongtime behavior of a second order finite element scheme simulating the kinematic effects in liquid crystal dynamics
Author(s) -
Mouhamadou Samsidy Goudiaby,
Ababacar Diagne,
Léon Matar Tine
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021116
Subject(s) - finite element method , liquid crystal , convergence (economics) , infinity , kinematics , mathematics , subspace topology , mathematical analysis , scheme (mathematics) , sequence (biology) , flow (mathematics) , geometry , physics , classical mechanics , genetics , biology , optics , economics , thermodynamics , economic growth
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.