Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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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.

Asymptotic exactness of some Bank--Weiser error estimator for quadratic triangular finite element

Kwang-Yeon Kim, Ju-Seong Park

Kangwon National University; Kangwon National University

Abstract

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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