A four-field mixed finite element method for Biot's consolidation problems (Q2030427)

This work discusses four-field mixed finite element method for Biot's consolidation problems. The four fields include the displacement, total stress, flux and pressure for the porous medium component of the modeling system. The approach combines a mixed finite element method involving Raviart-Thomas element for the fluid flow equation with the Crank-Nicolson scheme for the time discretization. The authors obtain optimal order error estimates for semi-discrete and fully discrete schemes for the unknowns in energy norm as well as \(L^2\) norm. Numerical experiments are included to support the theoretical findings.