A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bonetti, Stefano, Botti, Michele, Vega, Patrick
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908704905887744
author Bonetti, Stefano
Botti, Michele
Vega, Patrick
author_facet Bonetti, Stefano
Botti, Michele
Vega, Patrick
contents In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly-imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials.
format Preprint
id arxiv_https___arxiv_org_abs_2512_10192
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity
Bonetti, Stefano
Botti, Michele
Vega, Patrick
Numerical Analysis
65N15, 65N30
In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the symmetry constraint on the stress field is imposed via penalization. This strategy is equivalent to adding a perturbation to the saddle point system arising when the stress symmetry is weakly-imposed. The coupling of solid and fluid phases is discretized by means of stable mixed elements in space and implicit time advancing schemes. The presented stability analysis is fully robust with respect to meaningful cases of degenerate model parameters. Numerical tests validate the convergence and robustness and assess the performances of the method for the simulation of wave propagation phenomena in porous materials.
title A robust fully-mixed finite element method with skew-symmetry penalization for low-frequency poroelasticity
topic Numerical Analysis
65N15, 65N30
url https://arxiv.org/abs/2512.10192