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IMA Journal of Numerical Analysis 2001 21(3):643-665; doi:10.1093/imanum/21.3.643
© 2001 by Institute of Mathematics and its Applications
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Superconvergent derivative recovery for the intermediate finite element family of the second type

Zhimin Zhang1, Ningning Yan2 and Tong Sun3

1 Department of Mathematics, Wayne State University, Detroit, MI 48202, USA. Email: zzhang@math.wayne.edu 2 The Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China 3 Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH 43403, USA

In this work, a recovery technique for the intermediate finite element family of the second type is proposed and analysed on a second-order elliptic model problem. It is shown that when the pollution error is properly controlled, the convergence rate of the recovered gradient is two orders higher than the optimal global rate on an interior subdomain where rectangular meshes of regular type are applied. Some numerical results are provided to confirm the theoretical findings.

Key Words: finite element methods; integral identity; superconvergent recovery; intermediate family


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