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

TL;DR

This paper introduces a new fully-mixed finite element method for low-frequency poroelasticity that enforces stress symmetry via penalization, ensuring stability and robustness in wave propagation simulations.

Contribution

The work develops a novel finite element scheme with skew-symmetry penalization for stress, providing stability analysis and validation for low-frequency poroelastic wave modeling.

Findings

Method is stable and robust across degenerate parameters

Numerical tests confirm convergence and accuracy

Effective in simulating wave propagation in porous materials

Abstract

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.