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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Bibliographic Details
Published inMathematical modelling and analysis Vol. 26; no. 4; pp. 684 - 695
Main Authors Chaskalovic, Jöel, Assous, Franck
Format Journal Article
LanguageEnglish
Published Vilnius Vilnius Gediminas Technical University 26.11.2021
Taylor&Francis and VGTU
Subjects
Accuracy
Approximation
Asymptotic methods
bramble-hilbert lemma
Combinatorial probabilities
Error analysis
Error analysis (Mathematics)
error estimates
Estimates
Finite element method
finite elements
Geometric probabilities
Mathematical research
Mathematics
Numerical analysis
Numerical methods
numerical validation
Polynomials
Probabilities
probability
Random variables
France
Bramble-Hilbert lemma
error estimates
numerical validation
probability
finite elements
probability AMS Subject Classification: 65N15
65Gxx
65N30
65N75
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1392-6292
1648-3510
DOI:10.3846/mma.2021.14079