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Advances in Numerical Analysis
Volume 2015 (2015), Article ID 187604, 7 pages
Research Article

Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System

School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, NSW 2308, Australia

Received 24 June 2014; Revised 15 December 2014; Accepted 31 December 2014

Academic Editor: Slimane Adjerid

Copyright © 2015 Bishnu P. Lamichhane and Adam McNeilly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A gradient recovery operator based on projecting the discrete gradient onto the standard finite element space is considered. We use an oblique projection, where the test and trial spaces are different, and the bases of these two spaces form a biorthogonal system. Biorthogonality allows efficient computation of the recovery operator. We analyze the approximation properties of the gradient recovery operator. Numerical results are presented in the two-dimensional case.