Search arXivSearch

arXiv · 2504.06763

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

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.

Explore related subjects

Keep this discovery

BibTeXRIS

Jakob S. Stokke, Markus Bause, Florin A. Radu. 2026-09-05. Convergence of a continuous Galerkin method for the Biot-Allard poroelasticity system. https://arxiv.org/abs/2504.06763

Cite the original work for its findings. Save a collection to share your selection of sources.

Discover connections

Connections use source metadata and explicit phrase matches, not verified experimental comparisons.

KEEP EXPLORING

Related papers

Numerical experiments on the Hardy conjecture for the Gauss circle problem

The classical unsolved Gauss circle problem concerns estimating the error between the number of lattice points inside a circle and the area of the circle as its radius tends to infinity. About a century ago, Hardy proposed a conjecture concerning this problem. In this paper, we attempt to provide numerical evidence in support of the Hardy conjecture through large-scale numerical computations.

math.NT