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See detailHierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS Project
Bulle, Raphaël UL; Hale, Jack UL; Lozinski, Alexei et al

E-print/Working paper (2021)

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 ... [more ▼]

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. [less ▲]

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See detailRemoving the saturation assumption in Bank-Weiser error estimator analysis in dimension three
Bulle, Raphaël UL; Chouly, Franz; Hale, Jack UL et al

in Applied Mathematics Letters (2020), 107

We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes ... [more ▼]

We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case. [less ▲]

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See detailPractical aspects of the Bank-Weiser estimator implementation and Biomechanics applications.
Bulle, Raphaël UL; Bordas, Stéphane UL; Chouly, Franz et al

Scientific Conference (2020, July)

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See detailUncertainty Quantification in Finite Element Models:Application to SoftTissue Biomechanics
Hauseux, Paul UL; Hale, Jack UL; Bulle, Raphaël UL et al

Scientific Conference (2018, July 23)

We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree ... [more ▼]

We present probabilistic approaches aiming at the selection of the best constitutive model and to identify their parameters from experimental data. These parameters are always associated with some degree of uncertainty. It is therefore important to study how this statistical uncertainty in parameters propagates to a safety-critical quantity of interest in the output of a model. Efficient Monte Carlo methods based on variance reduction techniques (Sensitivity Derivatives Monte Carlo methods [Hauseux et al. 2017] and MultiLevel Monte Carlo [Giles 2015] methods) are employed to propagate this uncertainty for both random variables and random fields. Inverse and forward problems are strongly connected. In a bayesian setting [Matthies et al. 2017], developing methods that reduce the number of evaluations of the forward model to an absolute minimum to achieve convergence is crucial for tractable computations. Numerical results in the context of soft tissue biomechanics are presented and discussed. [less ▲]

Detailed reference viewed: 233 (7 UL)