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Volume 19, Issue 1
Optimal Mixed $H-P$ Finite Element Methods for Stokes and Non-Newtonian Flow

Ping-Bing Ming & Zhong-Ci Shi

J. Comp. Math., 19 (2001), pp. 67-76.

Published online: 2001-02

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  • Abstract

Based upon a new mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow, an $h-p$ finite element method is presented with or without a stabilization. As to the variational formulation without stabilization, optimal error bounds in $h$ as well as in $p$ are obtained. As with stabilization, optimal error bounds are obtained which is optimal in $h$ and one order deterioration in $p$ for the pressure, that is consistent with numerical results in [9,12] and therefore solved the problem therein. Moreover, we proposed a stabilized formulation which is optimal in both $h$ and $p$.

  • Keywords

Mixed hp-finite element method, Non-Newtonian flow, Stabilisation, Scaled weak B-B inequality.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-19-67, author = {Ming , Ping-Bing and Shi , Zhong-Ci}, title = {Optimal Mixed $H-P$ Finite Element Methods for Stokes and Non-Newtonian Flow}, journal = {Journal of Computational Mathematics}, year = {2001}, volume = {19}, number = {1}, pages = {67--76}, abstract = {

Based upon a new mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow, an $h-p$ finite element method is presented with or without a stabilization. As to the variational formulation without stabilization, optimal error bounds in $h$ as well as in $p$ are obtained. As with stabilization, optimal error bounds are obtained which is optimal in $h$ and one order deterioration in $p$ for the pressure, that is consistent with numerical results in [9,12] and therefore solved the problem therein. Moreover, we proposed a stabilized formulation which is optimal in both $h$ and $p$.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8958.html} }
TY - JOUR T1 - Optimal Mixed $H-P$ Finite Element Methods for Stokes and Non-Newtonian Flow AU - Ming , Ping-Bing AU - Shi , Zhong-Ci JO - Journal of Computational Mathematics VL - 1 SP - 67 EP - 76 PY - 2001 DA - 2001/02 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8958.html KW - Mixed hp-finite element method, Non-Newtonian flow, Stabilisation, Scaled weak B-B inequality. AB -

Based upon a new mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow, an $h-p$ finite element method is presented with or without a stabilization. As to the variational formulation without stabilization, optimal error bounds in $h$ as well as in $p$ are obtained. As with stabilization, optimal error bounds are obtained which is optimal in $h$ and one order deterioration in $p$ for the pressure, that is consistent with numerical results in [9,12] and therefore solved the problem therein. Moreover, we proposed a stabilized formulation which is optimal in both $h$ and $p$.

Ming , Ping-Bing and Shi , Zhong-Ci. (2001). Optimal Mixed $H-P$ Finite Element Methods for Stokes and Non-Newtonian Flow. Journal of Computational Mathematics. 19 (1). 67-76. doi:
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