A coupling of hybrid mixed and continuous Galerkin finite element methods for poroelasticity

摘要

A coupling finite element method for Biot’s model in poroelasticity is considered. The method is based on a coupling of a hybrid mixed finite element method for the pressure and velocity of the fluid phase with a continuous Galerkin finite element method for the displacement of the solid phase. The subproblem for pressure and Darcy velocity are solved at element level and these variables are eliminated in favor of the Lagrange multiplier, identified as pressure trace at the element interfaces. The method is consistent and locally mass conservative. By introducing the energy norm, we can obtain the stability of this system. The optimal error estimates are derived for both semi discrete and fully discrete schemes. Finally, numerical results illustrate the accuracy of the method.