Numerical validation of probabilistic laws to evaluate finite element error estimates

We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the t...

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Autores principales:	Jöel Chaskalovic, Franck Assous
Formato:	article
Lenguaje:	EN
Publicado:	Vilnius Gediminas Technical University 2021
Materias:	numerical validation error estimates finite elements bramble-hilbert lemma probability Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0b886095559a4d3dbbc82abc0ed78705
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id	oai:doaj.org-article:0b886095559a4d3dbbc82abc0ed78705
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spelling	oai:doaj.org-article:0b886095559a4d3dbbc82abc0ed787052021-11-29T09:14:00ZNumerical validation of probabilistic laws to evaluate finite element error estimates1392-62921648-351010.3846/mma.2021.14079https://doaj.org/article/0b886095559a4d3dbbc82abc0ed787052021-11-01T00:00:00Zhttps://journals.vgtu.lt/index.php/MMA/article/view/14079https://doaj.org/toc/1392-6292https://doaj.org/toc/1648-3510We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.Jöel ChaskalovicFranck AssousVilnius Gediminas Technical Universityarticlenumerical validationerror estimatesfinite elementsbramble-hilbert lemmaprobabilityMathematicsQA1-939ENMathematical Modelling and Analysis, Vol 26, Iss 4, Pp 684-695 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	numerical validation error estimates finite elements bramble-hilbert lemma probability Mathematics QA1-939
spellingShingle	numerical validation error estimates finite elements bramble-hilbert lemma probability Mathematics QA1-939 Jöel Chaskalovic Franck Assous Numerical validation of probabilistic laws to evaluate finite element error estimates
description	We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements Pk and Pm,(k < m). In particular, we show practical cases where finite element Pk gives more accurate results than finite element Pm. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.
format	article
author	Jöel Chaskalovic Franck Assous
author_facet	Jöel Chaskalovic Franck Assous
author_sort	Jöel Chaskalovic
title	Numerical validation of probabilistic laws to evaluate finite element error estimates
title_short	Numerical validation of probabilistic laws to evaluate finite element error estimates
title_full	Numerical validation of probabilistic laws to evaluate finite element error estimates
title_fullStr	Numerical validation of probabilistic laws to evaluate finite element error estimates
title_full_unstemmed	Numerical validation of probabilistic laws to evaluate finite element error estimates
title_sort	numerical validation of probabilistic laws to evaluate finite element error estimates
publisher	Vilnius Gediminas Technical University
publishDate	2021
url	https://doaj.org/article/0b886095559a4d3dbbc82abc0ed78705
work_keys_str_mv	AT joelchaskalovic numericalvalidationofprobabilisticlawstoevaluatefiniteelementerrorestimates AT franckassous numericalvalidationofprobabilisticlawstoevaluatefiniteelementerrorestimates
_version_	1718407385636143104

Numerical validation of probabilistic laws to evaluate finite element error estimates

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