Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project

[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 :

1873-7668

Publisher :

Elsevier, Oxford, United Kingdom

Volume :

131

Pages :

103-123

Peer reviewed :

Peer reviewed

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]

Available on ORBilu :

since 13 March 2021

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