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On the Euler implicit/explicit iterative scheme for the stationary Oldroyd fluid
Author(s) -
Guo Yingwen,
He Yinnian
Publication year - 2018
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22238
Subject(s) - mathematics , backward euler method , discretization , uniqueness , euler's formula , stability (learning theory) , explicit and implicit methods , euler equations , mathematical analysis , euler method , finite element method , semi implicit euler method , numerical analysis , ordinary differential equation , differential equation , collocation method , computer science , physics , machine learning , thermodynamics
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 ¯ , p ¯ } for the stationary equations and the almost unconditional stability of the numerical method. Furthermore, we also obtain the uniform optimalH 1andL 2error estimates in time integral 0 ≤ t < + ∞ . Finally, several numerical experiments are provided to verify our theoretical results.