Equal Lower-order Finite Elements of Least-squares Type in Biot Poroelasticity Modeling

We investigate the behavior of approximate solution Biot's consolidation model using a weighted least-squares (WLS) finite element method. The describes fluid flow in deformable porous medium, with variables for pressure, velocity, and displacement. WLS functional is defined based on stress-displacement formulation, symmetry condition stress weight that depends time step size temporal discretization model. An priori error estimate first-order linearized least squares (LS) system analyzed, its validity confirmed through numerical results. By continuous piecewise linear spaces all adjusting appropriately, we obtain optimal convergence rates variables. Additionally, present two examples to demonstrate implementation method benchmark problems.