Volume 10, Issue 2
On Fully Discrete Finite Element Schemes for Equations of Motion of Kelvin-Voigt Fluids

S. Bajpai, N. Nataraj & A. Pani

Int. J. Numer. Anal. Mod., 10 (2013), pp. 481-507

Published online: 2013-10

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  • Abstract
In this paper, we study two fully discrete schemes for the equations of motion arising in the Kelvin-Voigt model of viscoelastic uids. Based on a backward Euler method in time and a finite element method in spatial direction, optimal error estimates which exhibit the exponential decay property in time are derived. In the later part of this article, a second order two step backward di erence scheme is applied for temporal discretization and again exponential decay in time for the discrete solution is discussed. Finally, a priori error estimates are derived and results on numerical experiments conforming theoretical results are established.
  • Keywords

Viscoelastic uids Kelvin-Voigt model a priori bounds backward Euler method second order backward di erence scheme optimal error estimates

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@Article{IJNAM-10-481, author = {S. Bajpai, N. Nataraj and A. Pani}, title = {On Fully Discrete Finite Element Schemes for Equations of Motion of Kelvin-Voigt Fluids}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {2}, pages = {481--507}, abstract = {In this paper, we study two fully discrete schemes for the equations of motion arising in the Kelvin-Voigt model of viscoelastic uids. Based on a backward Euler method in time and a finite element method in spatial direction, optimal error estimates which exhibit the exponential decay property in time are derived. In the later part of this article, a second order two step backward di erence scheme is applied for temporal discretization and again exponential decay in time for the discrete solution is discussed. Finally, a priori error estimates are derived and results on numerical experiments conforming theoretical results are established.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/579.html} }
TY - JOUR T1 - On Fully Discrete Finite Element Schemes for Equations of Motion of Kelvin-Voigt Fluids AU - S. Bajpai, N. Nataraj & A. Pani JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 481 EP - 507 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/579.html KW - Viscoelastic uids KW - Kelvin-Voigt model KW - a priori bounds KW - backward Euler method KW - second order backward di erence scheme KW - optimal error estimates AB - In this paper, we study two fully discrete schemes for the equations of motion arising in the Kelvin-Voigt model of viscoelastic uids. Based on a backward Euler method in time and a finite element method in spatial direction, optimal error estimates which exhibit the exponential decay property in time are derived. In the later part of this article, a second order two step backward di erence scheme is applied for temporal discretization and again exponential decay in time for the discrete solution is discussed. Finally, a priori error estimates are derived and results on numerical experiments conforming theoretical results are established.
S. Bajpai, N. Nataraj & A. Pani. (1970). On Fully Discrete Finite Element Schemes for Equations of Motion of Kelvin-Voigt Fluids. International Journal of Numerical Analysis and Modeling. 10 (2). 481-507. doi:
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