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.

The Convergence of Coupled Boundary-Layer Equation in the Contact Interface

2014 ◽  
Vol 654 ◽  
pp. 283-286
Author(s):  
Lei Hou ◽  
N. Faraz ◽  
X.Y. Sun ◽  
J.J. Zhao ◽  
L. Qiu
Keyword(s):  
Boundary Layer ◽  
Finite Element Method ◽  
Finite Element ◽  
Boundary Layer Equation ◽  
Cauchy Equation ◽  
Galerkin Finite Element ◽  
Coupled Equations ◽  
Discrete Finite Element ◽  
Coupled Equation ◽  
Element Method

This paper introduces two equations of non-Newtonian boundary-layer fluid: Cauchy equation of flow field and P-T/T equation of stress field. Secondly, we analyze the convergence of this system of fluid-solid coupled equation with semi-discrete finite element method. We use Galerkin finite element method on the space and semi-implicit C-N difference scheme on the time. Thus, the convergent order of the coupled equations is O（h2+k2） .

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