Optimal Hessian recovery using a biorthogonal system with an application to adaptive refinement

Title: Optimal Hessian recovery using a biorthogonal system with an application to adaptive refinement
Creator: Shaw-Carmody, Jordan; Lamichhane, Bishnu
Relation: ANZIAM Journal Vol. 64, p. C130-C147
Publisher Link: http://dx.doi.org/10.21914/anziamj.v64.17971
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2024
Description: We present a method for recovering the Hessian from a linear finite element approach to achieve a higher rate of convergence. This method uses an L2 - based projection as well as boundary modification to achieve and improve the convergence rate. The projection uses a biorthogonal system to make the computation more numerically efficient. We present numerical examples to illustrate the efficiency and optimality of our approach on different meshes. The performance of our approach on adaptively refined meshes is briefly explored.
Subject: Hessian recovery; biorthogonal projection; boundary modification; adaptive finite element
Identifier: http://hdl.handle.net/1959.13/1506703
Identifier: uon:55923
Identifier: ISSN:1446-1811
Language: eng
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