Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system
Numerical Analysis
2025-04-10 v1 Numerical Analysis
Abstract
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.
Keywords
Cite
@article{arxiv.2504.06763,
title = {Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system},
author = {Jakob S. Stokke and Markus Bause and Florin A. Radu},
journal= {arXiv preprint arXiv:2504.06763},
year = {2025}
}