A first-order semi-implicit finite element method for nonlinear poroelastic flow is shown to have unique solutions and to converge at optimal rates when the nonlinear strain-stress perturbation is sufficiently small.
On a hierarchy of approximate models for flows of incompress- ible fluids through porous solids.Mathematical Models and Methods in Applied Sciences, 17(02):215–252
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Error analysis for the approximation of a flow in deformable porous media with nonlinear strain-stress relation
A first-order semi-implicit finite element method for nonlinear poroelastic flow is shown to have unique solutions and to converge at optimal rates when the nonlinear strain-stress perturbation is sufficiently small.