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.
Continuum theories of mixtures: applications.IMA Journal of Applied Mathematics, 17(2):153–207
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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.