Fully discrete finite element scheme for nonlocal parabolic problem involving the Dirichlet energy

2015 ◽  
Vol 53 (1-2) ◽  
pp. 413-443 ◽  
Author(s):  
Vimal Srivastava ◽  
Sudhakar Chaudhary ◽  
V. V. K. Srinivas Kumar ◽  
Balaji Srinivasan
Keyword(s):  
Finite Element ◽  
Parabolic Problem ◽  
Dirichlet Energy ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Fully Discrete ◽  
Discrete Finite Element

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>

Finite Element Scheme with Crank–Nicolson Method for Parabolic Nonlocal Problems Involving the Dirichlet Energy

2016 ◽  
Vol 14 (05) ◽  
pp. 1750053
Author(s):  
Sudhakar Chaudhary ◽  
Vimal Srivastava ◽  
V. V. K. Srinivas Kumar
Keyword(s):  
Finite Element ◽  
A Priori ◽  
Parabolic Problems ◽  
Dirichlet Energy ◽  
Weak Formulation ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Fully Discrete ◽  
Priori Error Estimates ◽  
Crank Nicolson

In this paper, we present a finite element scheme with Crank–Nicolson method for solving nonlocal parabolic problems involving the Dirichlet energy. We discuss the well-posedness of the weak formulation at continuous as well as at discrete levels. We derive a priori error estimates for both semi-discrete and fully-discrete formulations. Results based on usual finite element method are provided to confirm the theoretical estimates.

scholarly journals Superconvergence of finite element method for parabolic problem

2000 ◽  
Vol 23 (8) ◽  
pp. 567-578 ◽  
Author(s):  
Do Y. Kwak ◽  
Sungyun Lee ◽  
Qian Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Parabolic Problem ◽  
Higher Order ◽  
Initial Condition ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Discrete Finite Element ◽  
Element Method

We study superconvergence of a semi-discrete finite element scheme for parabolic problem. Our new scheme is based on introducing different approximation of initial condition. First, we give a superconvergence ofuh−Rhu, then use a postprocessing to improve the accuracy to higher order.

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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