Convergence Analysis of H(div)-Conforming Finite Element Methods for a Nonlinear Poroelasticity Problem - Yuping Zeng; Zhifeng Weng; Fen Liang (Discrete Dynamics in Nature and Society)
In this paper, we introduce and analyze H(div)-conforming finite element methods for a nonlinear model in poroelasticity. More precisely, the flow variables are discretized by H(div)-conforming mixed finite elements, while the elastic displacement is approximated by the H(div)-conforming finite element with the interior penalty discontinuous Galerkin formulation. Optimal a priori error estimates are derived for both semidiscrete and fully discrete schemes.