A multigrid method for the maximal correlation problem
Xin-Guo Liu Kun Wang
In this note, the continuity results of weak vector solutions and global vector solutions to a parametric generalized Ky Fan inequality are established by using a new scalarization method. Our results improve the corresponding ones of Li and Fang (J. Optim. Theory Appl. 147: 507-515, 2010).
keywords: alternating projection method starting point. correlation Multivariate statistics maximal correlation problem multivariate eigenvalue problem Horst method global solution Gauss-Seidel method
Long time numerical stability and asymptotic analysis for the viscoelastic Oldroyd flows
Kun Wang Yinnian He Yanping Lin
In this article, we study the long time numerical stability and asymptotic behavior for the viscoelastic Oldroyd fluid motion equations. Firstly, with the Euler semi-implicit scheme for the temporal discretization, we deduce the global $H^2-$stability result for the fully discrete finite element solution. Secondly, based on the uniform stability of the numerical solution, we investigate the discrete asymptotic behavior and claim that the viscoelastic Oldroyd problem converges to the stationary Navier-Stokes flows if the body force $f(x,t)$ approaches to a steady-state $f_\infty(x)$ as $t\rightarrow\infty$. Finally, some numerical experiments are given to verify the theoretical predictions.
keywords: Oldroyd model Viscoelastic flows asymptotic analysis. $H^2-$stability long time behavior
Fully discrete finite element method for the viscoelastic fluid motion equations
Kun Wang Yinnian He Yueqiang Shang
In this article, a fully discrete finite element method is considered for the viscoelastic fluid motion equations arising in the two-dimensional Oldroyd model. A finite element method is proposed for the spatial discretization and the time discretization is based on the backward Euler scheme. Moreover, the stability and optimal error estimates in the $L^2$- and $H^1$-norms for the velocity and $L^2$-norm for the pressure are derived for all time $t>0.$ Finally, some numerical experiments are shown to verify the theoretical predictions.
keywords: time discretization finite element method Viscoelastic fluid motion equations long-time error estimate. Oldroyd model
Asymptotic analysis of the equations of motion for viscoelastic oldroyd fluid
Kun Wang Yangping Lin Yinnian He
In this paper, the asymptotic analysis of the two-dimensional viscoelastic Oldroyd flows is presented. With the physical constant $\rho/\delta$ approaches zero, where $\rho$ is the viscoelastic coefficient and $1/\delta$ the relaxation time, the viscoelastic Oldroyd fluid motion equations converge to the viscous model known as the famous Navier-Stokes equations. Both the continuous and discrete uniform-in-time asymptotic errors are provided. Finally, the theoretical predictions are confirmed by some numerical experiments.
keywords: Viscoelastic flows long time behavior Oldroyd model asymptotic behavior Navier-Stokes equations.

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