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Journal Articles Computers & Mathematics with Applications Year : 2023

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

Raphaël Bulle
  • Function : Author
Jack S Hale
  • Function : Author
Alexei Lozinski
Stéphane P.A. Bordas
Franz Chouly

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.
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Dates and versions

hal-03137595 , version 1 (10-02-2021)

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Raphaël Bulle, Jack S Hale, Alexei Lozinski, Stéphane P.A. Bordas, Franz Chouly. Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project. Computers & Mathematics with Applications, 2023, 131, pp.103-123. ⟨10.1016/j.camwa.2022.11.009⟩. ⟨hal-03137595⟩
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