Numerical Validation of Probabilistic Laws to Evaluate Finite Element Error Estimates

Jöel Chaskalovic (1, 2) , Franck Assous (3)

1 SU - Sorbonne Université
2 DALEMBERT - Institut Jean Le Rond d'Alembert
3 Ariel University

We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements P k and Pm, (k < m). In particular, we show practical cases where finite element P k 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.

Mots clés: Numerical validation; Error estimates; Finite elements; Bramble-Hilbert lemma; Probability; 65N30; 65N75; 65Gxx; 65N15

Domaines: Analyse numérique [math.NA]; Applications [stat.AP]; Probabilités [math.PR]

Jöel Chaskalovic, Franck Assous. Numerical Validation of Probabilistic Laws to Evaluate Finite Element Error Estimates. Mathematical Modelling and Analysis, 2021, 26, pp.684 - 695. ⟨10.3846/mma.2021.14079⟩. ⟨hal-03832211⟩