On the Euler implicit/explicit iterative scheme for the stationary Oldroyd fluid

作者：Guo, Yingwen; He, Yinnian^*

来源：Numerical Methods for Partial Differential Equations, 2018, 34(3): 906-937.

DOI：10.1002/num.22238

• Euler implicit
• explicit scheme
• right-hand rectangle rule
• uniform optimal error estimates
• viscoelastic Oldroyd fluid

In this article, we consider the stationary Oldroyd fluid equations from the large time behavior research of the nonstationary equations. Thus, to obtain its numerical solution, we first solve the nonstationary Oldroyd fluid equations via the Euler implicit/explicit finite element method with the integral term discretized by the right-hand rectangle rule, then increase the total time (i.e., number of time steps) to approximate the solution of the original stationary equations. Under a new uniqueness condition (A2), we prove the exponential stability of the solution pair {(u) over bar, (p) over bar} for the stationary equations and the almost unconditional stability of the numerical method. Furthermore, we also obtain the uniform optimal H-1 and L-2 error estimates in time integral 0 <= t < + infinity. Finally, several numerical experiments are provided to verify our theoretical results.

• 出版日期2018-5
• 单位西安交通大学