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.
Domains
Numerical Analysis [math.NA]
Origin : Files produced by the author(s)