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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 fluids. 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 difference 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 fluids, Kelvin-Voigt model, a priori bounds, backward Euler method, second order backward difference scheme, optimal error estimates.

  • AMS Subject Headings

65M60,65M12,65M15,35D05,35D10

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@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 fluids. 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 difference 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 fluids, Kelvin-Voigt model, a priori bounds, backward Euler method, second order backward difference scheme, 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 fluids. 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 difference 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 and A. Pani. (2013). 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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