Residual-based a posteriori error estimates of mixed methods for a three-field Biot's consolidation model

TL;DR

This paper develops residual-based a posteriori error estimates for mixed finite element methods applied to the three-field Biot's consolidation model, providing bounds on discretization errors and extending to heat equation estimates.

Contribution

It introduces new residual-based a posteriori error estimators for the three-field Biot's model and derives bounds that include data oscillation effects.

Findings

Error estimators are both upper and lower bounds of the discretization error.

New a posteriori error estimate for mixed finite element methods for the heat equation.

Estimates account for data oscillation in the error bounds.

Abstract

We present residual-based a posteriori error estimates of mixed finite element methods for the three-field formulation of Biot's consolidation model. The error estimator is an upper and lower bound of the space time discretization error up to data oscillation. As a by-product, we also obtain new a posteriori error estimate of mixed finite element methods for the heat equation.