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L2-Norm Based a Posteriori Error Estimates of Compressible and Nearly-Incompressible Elastic Finite Element Solutions

Authors :
Mohd. Ahmed
Devinder Singh
Saeed AlQadhi
Nabil Ben Kahla
Source :
Applied Sciences, Vol 12, Iss 8, p 3999 (2022)
Publication Year :
2022
Publisher :
MDPI AG, 2022.

Abstract

The displacement and stress-based error estimates in a posteriori error recovery of compressible and nearly-incompressible elastic finite element solutions is investigated in the present study. The errors in the finite element solutions, i.e., in displacement and stress, at local and global levels are computed in L2-norm of quantity of interest, namely, displacements and gradients. The error estimation techniques are based on the least square fitting of higher order polynomials to stress and displacement in a patch comprising of node/elements surrounding and including the node/elements under consideration. The benchmark examples of compressible and incompressible elastic bodies, with known solutions employing triangular discretization schemes, are implemented to measure the finite element errors in displacements and gradients. The mixed formulation involving displacement and pressure is used for incompressible elastic analysis. The performance of error estimation is measured in terms of convergence properties, effectivity and mesh required for predefined precision. The error convergence rate, in FEM original solution, recovered solution using displacement recovery-based and stress-based error recovery technique for stresses, are obtained as (1.9714, 2.8999, and 2.5018) and (0.9818, 1.7805, and 1.4952) respectively for compressible and incompressible self-loaded elastic plate benchmark example using higher order triangular elements. It is concluded from the study that displacement fitting technique for extracting higher order derivatives shows a very effective technique for recovery of compressible and nearly-incompressible finite element analysis errors.

Details

Language :
English
ISSN :
20763417
Volume :
12
Issue :
8
Database :
Directory of Open Access Journals
Journal :
Applied Sciences
Publication Type :
Academic Journal
Accession number :
edsdoj.0ee611310b93496393fb6837de03f0d5
Document Type :
article
Full Text :
https://doi.org/10.3390/app12083999