Robust error analysis of coupled mixed methods for Biot's consolidation model
For researchers in computational geomechanics and poroelasticity, this work provides theoretical guarantees for mixed finite element methods that are robust under challenging material conditions.
This paper presents a robust a priori error analysis of coupled mixed finite element methods for Biot's consolidation model, achieving error estimates that are robust for material parameters such as nearly incompressible materials and without requiring a uniformly positive storage coefficient.
We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed finite elements, one for linear elasticity and the other for mixed Poisson problems are coupled for spatial discretization, and we show that any pair of stable mixed finite elements is available. The novelty of our analysis is that the error estimates of all the unknowns are robust for material parameters. Specifically, the analysis does not need a uniformly positive storage coefficient, and the error estimates are robust for nearly incompressible materials. Numerical experiments illustrating our theoretical analysis are included.