Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system

Fuente: arXiv
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Main Authors: Stokke, Jakob S., Bause, Markus, Radu, Florin A.
Format: Preprint
Published: 2025
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author Stokke, Jakob S.
Bause, Markus
Radu, Florin A.
author_facet Stokke, Jakob S.
Bause, Markus
Radu, Florin A.
contents We study a space-time finite element method for a system of poromechanics with memory effects that are modeled by a convolution integral. In the literature, the system is referred to as the Biot-Allard model. We recast the model as a first-order system in time, where the memory effects are transformed into an auxiliary differential equation. This allows for a computationally efficient numerical scheme. The system is discretized by continuous Galerkin methods in time and equal-order finite element methods in space. An optimal order error estimate is proved for the norm of the first-order energy of the unknowns of the system. The estimate is confirmed by numerical experiments.
format Preprint
id arxiv_https___arxiv_org_abs_2504_06763
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system
Stokke, Jakob S.
Bause, Markus
Radu, Florin A.
Numerical Analysis
We study a space-time finite element method for a system of poromechanics with memory effects that are modeled by a convolution integral. In the literature, the system is referred to as the Biot-Allard model. We recast the model as a first-order system in time, where the memory effects are transformed into an auxiliary differential equation. This allows for a computationally efficient numerical scheme. The system is discretized by continuous Galerkin methods in time and equal-order finite element methods in space. An optimal order error estimate is proved for the norm of the first-order energy of the unknowns of the system. The estimate is confirmed by numerical experiments.
title Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system
topic Numerical Analysis
url https://arxiv.org/abs/2504.06763