Poroelasticity modeling attracts researchers
from different areas and is of great importance not only in soil
mechanics but also in several applications in civil, petroleum and even
biomedical engineering. In this talk we consider the numerical solution of a
coupled fluid flow and geomechanics in Biot's consolidation model for
poroelasticity. The method combines mixed finite elements for Darcy flow and
Galerkin finite elements for elasticity. The numerical discretization of this
model gives rise to algorithmic challenges. Our focus is to discuss the
development of efficient and accurate numerical solutions, and give some
insight into the theoretical basis of the underlying methods. The fully coupled
approach solves flow and elasticity equations simultaneously. Alternatively,
operator splitting techniques can be used for solving the discrete system. The
choice of the coupling scheme affects the stability and accuracy of the
numerical solutions as well as the computational efficiency. In this talk we
discuss a priori convergence estimates for fully coupled schemes and for
iteratively coupled schemes. We perform numerical experiments for verifying our
theory and to compare different coupling techniques in engineering
applications.