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.
The elasticity of elasticity.Zeitschrift f¨ ur angewandte Mathe- matik und Physik, 58(2):309–317, 2007
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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.