TY - JOUR T1 - Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows AU - Yang , Yang AU - Lei , Yanfang AU - Si , Zhiyong JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 311 EP - 332 PY - 2020 DA - 2020/12 SN - 13 DO - http://doi.org/10.4208/aamm.OA-2018-0169 UR - https://global-sci.org/intro/article_detail/aamm/18486.html KW - Unconditional stability, optimal error estimates, modified characteristics finite element method, time-dependent viscoelastic Oldroyd flows. AB -

In this paper, our purpose is to study the unconditional stability and convergence of characteristics finite element method (FEM) for the time-dependent viscoelastic Oldroyd fluids motion equations. We deduce optimal error estimates in $L^2$ and $H^1$ norm. The analysis is based on an iterated time-discrete system, with which the error function is split into a temporal error and a spatial error. Finally, numerical results confirm the theoretical predictions.