Guaranteed locking-free finite element methods for Biot's consolidation model in poroelasticity

TL;DR

This paper introduces a new locking-free finite element method for Biot's consolidation model in poroelasticity, providing uniform error estimates without requiring positive storage coefficient assumptions.

Contribution

The paper presents a novel finite element approach that guarantees locking-free performance without the need for positive storage coefficient assumptions.

Findings

Achieves uniform-in-time error estimates for all unknowns.

Proves a priori error estimates for both semi-discrete and fully discrete solutions.

Method is robust without assumptions on the constrained specific storage coefficient.

Abstract

We propose a new finite element method for the three-field formulation of Biot's consolidation model in poroelasticity and prove a priori error estimates. Uniform-in-time error estimates of all the unknowns are obtained for both semidiscrete solutions and fully discrete solutions with the backward Euler time discretization. The novelty of our method is that the error analysis does not require the assumption that the constrained specific storage coefficient is uniformly positive. Therefore the method is guaranteed to be locking-free without the additional assumption on material parameters.