Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Abstract
In the seminal paper of Bank and Weiser [Math. Comp., 44 (1985), pp.283-301] 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 implementation of hierarchical estimators of the Bank-Weiser type 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 and to mixed approximations of the nearly-incompressible elasticity problems. We provide comparisons with various other used estimators. An open-source implementation based on the FEniCS Project finite element software is provided as supplementary material.
Keywords
Cite
@article{arxiv.2102.04360,
title = {Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project},
author = {Raphaël Bulle and Jack S. Hale and Alexei Lozinski and Stéphane P. A. Bordas and Franz Chouly},
journal= {arXiv preprint arXiv:2102.04360},
year = {2022}
}