Two-grid finite element scheme for the fully discrete time-dependent Navier–Stokes problem

2005 ◽  
Vol 341 (7) ◽  
pp. 451-456 ◽  
Author(s):  
Hyam Abboud ◽  
Vivette Girault ◽  
Toni Sayah
Keyword(s):  
Finite Element ◽  
Discrete Time ◽  
Stokes Problem ◽  
Time Dependent ◽  
Navier Stokes ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Fully Discrete

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>

scholarly journals Modeling of linear dispersive materials using scalable time domain finite element scheme

2016 ◽  
Vol 65 (4) ◽  
pp. 719-732
Author(s):  
Bogusław Butryło
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Time Dependent ◽  
Dispersive Media ◽  
Benchmark Problem ◽  
The Finite Element Method ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Convolution Integrals ◽  
Element Algorithm

Abstract This paper deals with some aspects of formulation and implementation of a broadband algorithm with build-in analysis of some dispersive media. The construction of the finite element method (FEM) based on direct integration of Maxwell’s equations and solution of some additional convolution integrals is presented. The broadband, fractional model of permittivity is approximated by a set of some relaxation sub-models. The properties of the 3D time-dependent formulation of the FEM algorithm are determined using a benchmark problem with the Cole-Cole and the Davidson-Cole models. Several issues associated with the implementation and some constraints of the broadband finite element algorithm are presented.

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