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Volume 13, Issue 2
Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows

Yang Yang, Yanfang Lei & Zhiyong Si

DOI: 10.4208/aamm.OA-2018-0169

Adv. Appl. Math. Mech., 13 (2021), pp. 311-332.

Published online: 2020-12

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  • Abstract

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.

  • Keywords

Unconditional stability, optimal error estimates, modified characteristics finite element method, time-dependent viscoelastic Oldroyd flows.

  • AMS Subject Headings

76M10, 65N12, 65N30, 35K61

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-13-311, author = {Yang , YangLei , Yanfang and Si , Zhiyong}, title = {Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2020}, volume = {13}, number = {2}, pages = {311--332}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0169}, url = {http://global-sci.org/intro/article_detail/aamm/18486.html} }
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.

Yang , YangLei , Yanfang and Si , Zhiyong. (2020). Unconditional Stability and Error Estimates of the Modified Characteristics FEM for the Time-Dependent Viscoelastic Oldroyd Flows. Advances in Applied Mathematics and Mechanics. 13 (2). 311-332. doi:10.4208/aamm.OA-2018-0169
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