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

2025/04/09 by Stokke, Jakob S., Bause, Markus, Radu, Florin A.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.06763

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.

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