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） .

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.

Semi-Discrete Galerkin Finite Element Method for the Diffusive Peterlin Viscoelastic Model

2018 ◽  
Vol 18 (2) ◽  
pp. 275-296 ◽  
Author(s):  
Yao-Lin Jiang ◽  
Yun-Bo Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Iterative Scheme ◽  
A Priori ◽  
Viscoelastic Model ◽  
Optimal Error Estimates ◽  
Galerkin Finite Element Method ◽  
Galerkin Finite Element ◽  
Discrete Finite Element ◽  
Element Method

AbstractIn this paper, a semi-discrete Galerkin finite element method is applied to the two-dimensional diffusive Peterlin viscoelastic model which can describe the unsteady behavior of some incompressible ploymeric fluids. For the derived semi-discrete finite element spatial discretization scheme, the a priori bounds are given that does not rely on the mesh width restriction. Further, with the help of the a priori error bounds of the Stokes and Ritz projections, optimal error estimates for the velocity, the conformation tensor and the pressure are presented, respectively. Finally, in order to implement the proposed semi-discrete numerical scheme, we derive three kinds of fully discrete schemes, e.g., Newton’s iterative scheme, Picard’s iterative scheme and implicit-explicit time-stepping scheme. Finally, several numerical experiments are conducted to confirm our theoretical results.

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