  This work proposes a mixed finite element method for the Biot poroelasticity
equations that employs the lowest-order Raviart-Thomas finite element space for
the solid displacement and piecewise constants for the fluid pressure. The
method is based on the formulation of linearized elasticity as a weighted
vector Laplace problem. By introducing the solid rotation and fluid flux as
auxiliary variables, we form a four-field formulation of the Biot system, which
is discretized using conforming mixed finite element spaces. The auxiliary
variables are subsequently removed from the system in a local hybridization
technique to obtain a multipoint rotation-flux mixed finite element method.
Stability and convergence of the four-field and multipoint mixed finite element
methods are shown in terms of weighted norms, which additionally leads to
parameter-robust preconditioners. Numerical experiments confirm the theoretical
results.
