2021/02/08 by Raphaël Bulle, Jack Hale, Bulle, Raphaël +7
Decision Sciences · Engineering · #Advanced Numerical Methods in Computational Mathematics #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Topology Optimization in Engineering #and Science (cs.CE)
paper · doi:10.48550/arxiv.2102.04360
openalex publication_date 2021/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.