We introduce a stress/total-pressure formulation for poroelasticity that includes the coupling with steady nonlinear diffusion modified by stress. The nonlinear problem is written in mixed-primal form, coupling a perturbed twofold saddle-point system with an elliptic problem. The continuous formulation is analysed in the framework of abstract fixed-point theory and Fredholm alternative for compact operators. A mixed finite element method is proposed and its stability and convergence analysis are carried out. We also include a few illustrative numerical tests. The resulting model can be used to study waste removal in the brain parenchyma, where diffusion of a tracer alone or a combination of advection and diffusion are not sufficient to explain the alterations in rates of filtration observed in porous media samples.

翻译：我们引入一种压力/总压力配方,以适应压力,包括结合稳定的非线性扩散,经压力改变; 非线性问题以混合原始形式写成,将受扰动的双马鞍点系统与椭圆形问题结合; 连续配方在抽象固定点理论和契约操作者Fredholm替代方法的框架内分析; 提出混合有限元素方法,并进行其稳定性和趋同性分析; 我们还包括几个说明性数字测试; 由此形成的模型可用于研究脑膜中废物的清除情况,在那里单靠痕量或吸附与扩散相结合不足以解释在多孔介质样本中观察到的过滤率的变化。