[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.
Research center :
ULHPC - University of Luxembourg: High Performance Computing
Disciplines :
Mathematics Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
BULLE, Raphaël ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
HALE, Jack ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Lozinski, Alexei
BORDAS, Stéphane ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Engineering (DoE)
Chouly, Franz
External co-authors :
yes
Language :
English
Title :
Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Publication date :
01 February 2023
Journal title :
Computers and Mathematics with Applications
ISSN :
0898-1221
eISSN :
1873-7668
Publisher :
Elsevier, Oxford, United Kingdom
Volume :
131
Pages :
103-123
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
European Projects :
H2020 - 811099 - DRIVEN - Increasing the scientific excellence and innovation capacity in Data-Driven Simulation of the University of Luxembourg
Funders :
ASSIST UL IRP I-Site BFC project NAANoD EIPHI Graduate School ANR-17-EURE-0002 CE - Commission Européenne [BE]
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