  In this paper, we aim at solving the Biot model under stabilized finite
element discretizations. To solve the resulting generalized saddle point linear
systems, some iterative methods are proposed and compared. In the first method,
we apply the GMRES algorithm as the outer iteration. In the second method, the
Uzawa method with variable relaxation parameters is employed as the outer
iteration method. In the third approach, Uzawa method is treated as a
fixed-point iteration, the outer solver is the so-called Anderson acceleration.
In all these methods, the inner solvers are preconditioners for the generalized
saddle point problem. In the preconditioners, the Schur complement
approximation is derived by using Fourier analysis approach. These
preconditioners are implemented exactly or inexactly. Extensive experiments are
given to justify the performance of the proposed preconditioners and to compare
all the algorithms.
