scholarly journals Fully discrete finite element method based on second-order Crank-Nicolson/Adams-Bashforth scheme for the equations of motion of Oldroyd fluids of order one

2015 ◽  
Vol 20 (8) ◽  
pp. 2583-2609 ◽  
Author(s):  
Yinnian He ◽  
Yingwen Guo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Equations Of Motion ◽  
Second Order ◽  
Fully Discrete ◽  
Discrete Finite Element ◽  
Element Method ◽  
Crank Nicolson

The Semi-Discrete Finite Element Method for the Cauchy Equation

2014 ◽  
Vol 668-669 ◽  
pp. 1130-1133
Author(s):  
Lei Hou ◽  
Xian Yan Sun ◽  
Lin Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Cauchy Equation ◽  
The Time Domain ◽  
Nicolson Scheme ◽  
Discrete Finite Element ◽  
Better Than ◽  
Element Method ◽  
Crank Nicolson

In this paper, we employ semi-discrete finite element method to study the convergence of the Cauchy equation. The convergent order can reach. In numerical results, the space domain is discrete by Lagrange interpolation function with 9-point biquadrate element. The time domain is discrete by two difference schemes: Euler and Crank-Nicolson scheme. Numerical results show that the convergence of Crank-Nicolson scheme is better than that of Euler scheme.

scholarly journals A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jinfeng Wang ◽  
Hong Li ◽  
Siriguleng He ◽  
Wei Gao ◽  
Yang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
A Priori ◽  
Mixed Finite Element Method ◽  
Order Equation ◽  
Second Order ◽  
Fully Discrete ◽  
Priori Error Estimates ◽  
Element Method

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient∇ubelongs to the weaker(L2(Ω))2space taking the place of the classicalH(div;Ω)space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates inL2andH1-norm for both the scalar unknownuand the diffusion termw=−Δuand a priori error estimates in(L2)2-norm for its gradientχ=∇ufor both semi-discrete and fully discrete schemes.

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