Numerical validation of probabilistic laws to evaluate finite element error estimates

• Published in: Mathematical modelling and analysis Vol. 26; no. 4; pp. 684 - 695
• Main Authors: Chaskalovic, Jöel, Assous, Franck
• Format: Journal Article
• Language: English
• 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

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...