Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates
Numerical approximation of generalized Newtonian fluids using Powell–Sabin–Heindl elements: I. theoretical estimates
复制标题
使用 Powell-Sabin-Heindl 元件对广义牛顿流体进行数值逼近：I. 理论估计
DOI：
10.1002/fld.480
复制
发表时间：
2003
影响因子：
1.8
通讯作者：
G. Carey
中科院分区：
文献类型：
--
作者：
S. Chow;G. Carey
本文考虑用Powell-Sabin-Heindl单元生成的无发散有限元数值逼近定常和非定常广义牛顿流体流动。我们推导出先验和后验有限元误差估计，并证明了定常流情况下的逐次逼近方法的收敛性。先验误差估计的非定常流也被认为是。这些结果提供了一个理论基础和支持的数值研究将在第二部分提供。版权所有© 2003年约翰威利父子有限公司。
In this paper we consider the numerical approximation of steady and unsteady generalized Newtonian fluid flows using divergence free finite elements generated by the Powell–Sabin–Heindl elements. We derive a priori and a posteriori finite element error estimates and prove convergence of the method of successive approximations for the steady flow case. A priori error estimates of unsteady flows are also considered. These results provide a theoretical foundation and supporting numerical studies are to be provided in Part II. Copyright © 2003 John Wiley & Sons, Ltd.