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

Ping Bing Ming & Zhong Ci Shi

DOI:

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

Mired hp-finite element method Non-Newtonian flow Stabilisation Scaled weak B-B ineq

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@Article{JCM-19-67, author = {}, 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 JO - Journal of Computational Mathematics VL - 1 SP - 67 EP - 76 PY - 2001 DA - 2001/02 SN - 19 DO - http://dor.org/ UR - https://global-sci.org/intro/article_detail/jcm/8958.html KW - Mired hp-finite element method KW - Non-Newtonian flow KW - Stabilisation KW - Scaled weak B-B ineq 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.
Ping Bing Ming & Zhong Ci Shi. (1970). 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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