Journal of the
Korean Mathematical Society
JKMS

ISSN(Print) 0304-9914 ISSN(Online) 2234-3008

Article

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J. Korean Math. Soc. 2015; 52(5): 891-906

Printed September 1, 2015

https://doi.org/10.4134/JKMS.2015.52.5.891

Copyright © The Korean Mathematical Society.

Postprocessing for guaranteed error bound based on equilibrated fluxes

Kwang-Yeon Kim

Kangwon National University

Abstract

In this work we analyze a postprocessing scheme for improving the guaranteed error bound based on the equilibrated fluxes for the $P1$ conforming FEM. The improved error bound is shown to be asymptotically exact under suitable conditions on the triangulations and the regularity of the true solution. We also present some numerical results to illustrate the effect of the postprocessing scheme.

Keywords: a posteriori error estimation, equilibrated fluxes, guaranteed error bound, asymptotic exactness, superconvergence

MSC numbers: Primary 65N30, 65N15