Hierarchical a posteriori error estimation of Bank–Weiser type in the FEniCS Project Article - Décembre 2022

Raphaël Bulle, Jack Hale, Alexei Lozinski, Stéphane P.A. Bordas, Franz Chouly

Raphaël Bulle, Jack Hale, Alexei Lozinski, Stéphane P.A. Bordas, Franz Chouly, « Hierarchical a posteriori error estimation of Bank–Weiser type in the FEniCS Project  », Computers & Mathematics with Applications, décembre 2022, pp. 103-123. ISSN 0898-1221. 〈https://www.sciencedirect.com/science/article/abs/pii/S0898122122004722〉

Abstract

In the seminal paper of Bank and Weiser (1985) [17] a new a posteriori estimator was introduced. This estimator requires the solution of a local Neumann problem on every cell of the finite element mesh. Despite the promise of Bank–Weiser type estimators, namely locality, computational efficiency, and asymptotic sharpness, they have seen little use in practical computational problems. The focus of this contribution is to describe a novel algorithmic approach to constructing hierarchical estimators of the Bank–Weiser type that is designed for implementation in a modern high-level finite element software with automatic code generation capabilities. We show how to use the estimator to drive (goal-oriented) adaptive mesh refinement for diverse Poisson problems and for mixed approximations of the nearly-incompressible elasticity problems. We provide comparisons with various other used estimators. Two open source implementations in the DOLFIN and DOLFINx solvers of the FEniCS Project are provided as supplementary material.

Voir la notice complète sur HAL

Actualités