Reference : Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
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http://hdl.handle.net/10993/46602
Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
English
Bulle, Raphaël mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
Hale, Jack mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
Lozinski, Alexei []
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE) >]
Chouly, Franz []
Feb-2021
No
[en] 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.
ASSIST UL IRP ; I-Site BFC project NAANoD ; EIPHI Graduate School ANR-17-EURE-0002
Researchers
http://hdl.handle.net/10993/46602
https://arxiv.org/abs/2102.04360
H2020 ; 811099 - DRIVEN - Increasing the scientific excellence and innovation capacity in Data-Driven Simulation of the University of Luxembourg

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