Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three

Raphal Bulle (1) , Franz Chouly (2) , Jack S Hale (1) , Alexei Lozinski (3)

1 University of Luxembourg [Luxembourg]
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 IMT - Institut de Mathématiques de Toulouse UMR5219

We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.

Mots clés: finite element methods; a posteriori error estimation; saturation assumption; Bank-Weiser estimator; residual estimator

Domaines: Analyse numérique [math.NA]

Raphal Bulle, Franz Chouly, Jack S Hale, Alexei Lozinski. Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three. 2020. ⟨hal-02482235v1⟩