Analysis and numerical approximations of equations of nonlinear poroelasticity

The equations of quasi-static poroelasticity which model flow through elastic porousmedia are considered. It is assumed that the hydraulic conductivitydepends nonlinearly on the displacement (the dilatation) of the medium. The existence of a weak solution is proved using the modified Rothe's method. Numerical approximations of solutions by the finite element method are considered. Error estimates are obtained and numericalexperiments are conducted to illustrate the theoretical results, and the efficiency and accuracyof the numerical method.