Internal wave reflections and transmissions arising from a non-uniform mesh. Part II: A generalized analysis for the Crank-Nicolson linear finite element scheme

1989 ◽  
Vol 9 (7) ◽  
pp. 811-832 ◽  
Author(s):  
B. Cathers ◽  
S. Bates ◽  
R. Penoyre ◽  
B. A. O'Connor
Keyword(s):  
Finite Element ◽  
Internal Wave ◽  
Uniform Mesh ◽  
Wave Reflections ◽  
Finite Element Scheme ◽  
Element Scheme ◽  
Linear Finite Element ◽  
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.

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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