  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.

Numerical Analysis;Computational Engineering, Finance, and Science;Numerical Analysis