In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized gradient flow structure, identifying the dissipative character of the physical system. The considered mixed finite element discretization is compatible with this structure, which gives access to a simple proof for the existence, uniqueness, and stability of discrete approximations. Moreover, still within the framework, the discretization allows for the development of finite volume type discretizations by lumping or numerical quadrature, reducing the computational cost of the numerical solution.

翻译：在本文中,我们为传统达西-福切海默传统不线性结合模型开发了一种分解模式,用于可变多孔介质中的典型达西-福赫海默流动,这是准静态生物方程式的延伸。连续模型展示了一种普遍的梯度流结构,确定了物理系统的消散特性。被考虑的混合有限元素分解与这一结构相容,这种结构使得人们能够获得一个简单的证据证明离散近点的存在、独特性和稳定性。 此外,在框架范围内,分解还允许通过组合或数字等式来发展有限的体型分解,从而降低数字解决方案的计算成本。