Stabilized multiphysics finite element method with Crank–Nicolson scheme for a poroelasticity model

Abstract

In the paper, we propose a stabilized multiphysics finite element method with Crank–Nicolson scheme for a poroelasticity model. The method can eliminate the locking phenomenon and reveal the multi‐physical process. The lowest equal order finite element pair is used to reduce the computational cost. Furthermore, the method needs no constraint condition Δt = O(h2) and achieves optimal convergent order. Numerical tests are provided to illustrate the optimal accuracy and good performance in eliminating locking phenomenon of the method.