Approximation Properties of a Gradient Recovery Operator Using a Biorthogonal System

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 com...

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Bibliographic Details
Published in:Advances in Numerical Analysis 2015-01, Vol.2015 (2015), p.a1-7
Main Authors: Lamichhane, Bishnu P., McNeilly, Adam
Format: Article
Language:English
Subjects:
Analysis
Approximation theory
Finite element analysis
Partial differential equations
Transformations (Mathematics)
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Summary: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.
ISSN:1687-9562
1687-9562
DOI:10.1155/2015/187604