Bull. Korean Math. Soc. 2020; 57(2): 393-406
Online first article February 25, 2020 Printed March 31, 2020
https://doi.org/10.4134/BKMS.b190278
Copyright © The Korean Mathematical Society.
Kwang-Yeon Kim, Ju-Seong Park
Kangwon National University; Kangwon National University
We analyze a posteriori error estimator for the conforming $P2$ finite element on triangular meshes which is based on the solution of local Neumann problems. This error estimator extends the one for the conforming $P1$ finite element proposed in \cite{Bank-Weiser85}. We prove that it is asymptotically exact for the Poisson equation when the underlying triangulations are mildly structured and the solution is smooth enough.
Keywords: A posteriori error estimator, asymptotic exactness, quadratic finite element method
MSC numbers: Primary 65N30, 65N15
Supported by: This study was supported by 2017 Research Grant from Kangwon National University (No. D1001531-01-01).
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