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Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

Abstract : In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the parameter-dependent problem by non-intrusive techniques based on Polynomial Chaos decompositions. We specifically focus on sparse spectral projection methods, which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients. The deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders. We numerically investigate the convergence of the probability error of the Polynomial Chaos approximation with respect to the level of the sparse grid. Finally, we assess the propagation of the input uncertainty onto the solution considering an injection-extraction problem.
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https://hal.archives-ouvertes.fr/hal-02081647
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Soumis le : lundi 11 novembre 2019 - 12:03:57
Dernière modification le : mardi 4 août 2020 - 15:30:23
Document(s) archivé(s) le : mercredi 12 février 2020 - 12:44:47

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Daniele A. Di Pietro, Michele Botti, Daniele Di Pietro, Olivier Le Maitre, Pierre Sochala. Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2020, 361, pp.112736. ⟨10.1016/j.cma.2019.112736⟩. ⟨hal-02081647v2⟩

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