An energy law preserving C0 finite element scheme for simulating the kinematic effects in liquid crystal dynamics

2007 ◽  
Vol 227 (2) ◽  
pp. 1411-1427 ◽  
Author(s):  
Ping Lin ◽  
Chun Liu ◽  
Hui Zhang
Keyword(s):  
Finite Element ◽  
Liquid Crystal ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Crystal Dynamics ◽  
Energy Law

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mouhamadou Samsidy Goudiaby ◽  
Ababacar Diagne ◽  
Leon Matar Tine
Keyword(s):  
Finite Element ◽  
Liquid Crystal ◽  
Type Inequality ◽  
Mesh Size ◽  
Time Step ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Fully Discrete ◽  
Discrete Finite Element ◽  
Longtime Behavior

<p style='text-indent:20px;'>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.</p>

An adaptive finite element scheme to solve fluid-structure vibration problems on non-matching grids

2001 ◽  
Vol 4 (2) ◽  
pp. 67-78 ◽  
Author(s):  
Ana Alonso ◽  
Anahí Dello Russo ◽  
César Otero-Souto ◽  
Claudio Padra ◽  
Rodolfo Rodríguez
Keyword(s):  
Finite Element ◽  
Adaptive Finite Element ◽  
Finite Element Scheme ◽  
Fluid Structure ◽  
Element Scheme ◽  
Structure Vibration ◽  
Vibration Problems
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