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 - <p style="text-align: justify;">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 $p$.</p>