An H(div)-Conforming Finite Element Method for the Biot Consolidation Model

: In this paper, we develop an H(div)-conforming finite element method for Biot's consolidation model in poroelasticity. In our method, the flow variables are discretized by an H(div)-conforming mixed finite elements. For relaxing the H1-conformity of the displacement, we approximate the displacement by using an H(div)-conforming finite element method, in which the tangential components are discretized in the interior penalty discontinuous Galerkin framework. For both the semi-discrete and the fully discrete schemes, we prove the existence and uniqueness theorems of the approximate solutions and derive the optimal convergence rate for each variable.