J. Korean Math. Soc. 2023; 60(2): 273-302
Online first article February 16, 2023 Printed March 1, 2023
https://doi.org/10.4134/JKMS.j210671
Copyright © The Korean Mathematical Society.
Huifang Zhang, Tong Zhang
Yantai University; Yantai University
In this paper, a fully discrete numerical scheme for the viscoelastic Oldroyd flow is considered with an introduced auxiliary variable. Our scheme is based on the finite element approximation for the spatial discretization and the backward Euler scheme for the time discretization. The integral term is discretized by the right trapezoidal rule. Firstly, we present the corresponding equivalent form of the considered model, and show the relationship between the origin problem and its equivalent system in finite element discretization. Secondly, unconditional stability and optimal error estimates of fully discrete numerical solutions in various norms are established. Finally, some numerical results are provided to confirm the established theoretical analysis and show the performances of the considered numerical scheme.
Keywords: The viscoelastic Oldroyd flow, unconditional stability, optimal error estimates
MSC numbers: Primary 65M10, 65N30, 76Q10
Supported by: This work was financially supported by NSF of China (No.11971152) and NSF of Henan Province (202300410167).
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