A coupling of mixed and Galerkin finite element methods for poro-elasticity

Abstract

This chapter discusses a finite element procedure for approximating the coupled fluid and mechanics in Biot's consolidation model of poro-elasticity. The pressure is approximated by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived. Of particular interest is the case when the lowest order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. Preliminary computational results confirm theoretical results for the case of continuous linears for displacement and cell-centered finite differences for pressure. Moreover, the modeling of coupled mechanics and flow in porous is of interest in reservoir engineering applications because most commercial simulators approximate the pressure equation by cell-centered finite differences.