scholarly journals On a two-grid finite element scheme combined with Crank–Nicolson method for the equations of motion arising in the Kelvin–Voigt model

2014 ◽  
Vol 68 (12) ◽  
pp. 2277-2291 ◽  
Author(s):  
S. Bajpai ◽  
N. Nataraj
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Voigt Model ◽  
Crank Nicolson

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 A Crank-Nicolson Scheme for the Dirichlet-to-Neumann Semigroup

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Rola Ali Ahmad ◽  
Toufic El Arwadi ◽  
Houssam Chrayteh ◽  
Jean-Marc Sac-Epée
Keyword(s):  
Exact Solution ◽  
Finite Element ◽  
Product Formula ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Nicolson Scheme ◽  
Crank Nicolson

The aim of this work is to study a semidiscrete Crank-Nicolson type scheme in order to approximate numerically the Dirichlet-to-Neumann semigroup. We construct an approximating family of operators for the Dirichlet-to-Neumann semigroup, which satisfies the assumptions of Chernoff’s product formula, and consequently the Crank-Nicolson scheme converges to the exact solution. Finally, we write aP1finite element scheme for the problem, and we illustrate this convergence by means of a FreeFem++ implementation.

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