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In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…

Numerical Analysis · Mathematics 2023-06-27 Wietse M. Boon , Martin Hornkjøl , Miroslav Kuchta , Kent-Andre Mardal , Ricardo Ruiz-Baier

We propose a novel cut finite element method for the numerical solution of the Biot system of poroelasticity. The Biot system couples elastic deformation of a porous solid with viscous fluid flow and commonly arises on domains with complex…

Numerical Analysis · Mathematics 2026-02-10 Nanna Berre , Kent-Andre Mardal , André Massing , Ivan Yotov

Accurate simulation of the coupled fluid flow and solid deformation in porous media is challenging, especially when the media permeability and storativity are heterogeneous. We apply the enriched Galerkin (EG) finite element method for the…

Computational Engineering, Finance, and Science · Computer Science 2023-08-30 T. Kadeethum , H. M. Nick , S. Lee , F. Ballarin

We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a…

Analysis of PDEs · Mathematics 2021-03-23 Lorena Bociu , Justin T. Webster

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filtration fluxes. The proposed method is based on the use of…

Numerical Analysis · Mathematics 2025-10-23 Ruben Caraballo , Chansophea Wathanak In , Alberto F. Martín , Ricardo Ruiz-Baier

We develop a mixed finite element method for the coupled problem arising in the interaction between a free fluid governed by the Stokes equations and flow in deformable porous medium modeled by the Biot system of poroelasticity. Mass…

Numerical Analysis · Mathematics 2021-12-16 Tongtong Li , Ivan Yotov

We study a thermo-poroelasticity model which describes the interaction between the deformation of an elastic porous material and fluid flow under non-isothermal conditions. The model involves several parameters that can vary significantly…

Numerical Analysis · Mathematics 2025-12-24 Mingchao Cai , Miroslav Kuchta , Jingzhi Li , Ziliang Li , Kent-Andre Mardal

This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and…

Numerical Analysis · Mathematics 2022-08-10 Shanshan Gu , Shimin Chai , Chenguang Zhou

The quasi-static multiple network poroelastic theory (MPET) model, first introduced in the context of geomechanics, has recently found new applications in medicine. In practice, the parameters in the MPET equations can vary over several…

Numerical Analysis · Mathematics 2022-05-16 Johannes Kraus , Philip L. Lederer , Maria Lymbery , Kevin Osthues , Joachim Schöberl

We study a finite element computational model for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium. The free fluid is governed by the Stokes equations, while the flow in the…

Numerical Analysis · Mathematics 2017-10-19 Ilona Ambartsumyan , Eldar Khattatov , Ivan Yotov , Paolo Zunino

We consider finite element discretizations of the Biot's consolidation model in poroelasticity with MINI and stabilized P1-P1 elements. We analyze the convergence of the fully discrete model based on spatial discretization with these types…

Numerical Analysis · Mathematics 2023-07-19 Carmen Rodrigo , Francisco Gaspar , Xiaozhe Hu , Ludmil Zikatanov

The mechanical behaviour of a poroelastic medium permeated by multiple interacting fluid networks can be described by a system of time-dependent partial differential equations known as the multiple-network poroelasticity (MPET) equations or…

Numerical Analysis · Mathematics 2020-10-20 Eleonora Piersanti , Jeonghun J. Lee , Travis Thompson , Kent-Andre Mardal , Marie E. Rognes

The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study complex poromechanical interactions in geophysics, biophysics…

Numerical Analysis · Mathematics 2021-12-28 Q. Hong , J. Kraus , M. Kuchta , M. Lymbery , K. A. Mardal , M. E. Rognes

We study a fluid-poroelasticity interaction (FPSI) problem coupling the unsteady Stokes equations with the fully dynamic Biot system. A major challenge in such problems is to design partitioned schemes that remain robust in locking-related…

Numerical Analysis · Mathematics 2026-04-13 Wenlong He , Thomas Wick , Xiaohe Yue , Jiwei Zhang , Haibiao Zheng

The focus of this work is a posteriori error estimation for stochastic Galerkin approximations of parameter-dependent linear elasticity equations. The starting point is a three-field PDE model in which the Young's modulus is an affine…

Numerical Analysis · Mathematics 2018-10-18 Arbaz Khan , Alex Bespalov , Catherine E. Powell , David J. Silvester

We consider Biot model with block preconditioners and generalized eigenvalue problems for scalability and robustness to parameters. A discontinuous Galerkin discretization is employed with the displacement and Darcy flow flux discretized as…

Numerical Analysis · Mathematics 2023-06-23 Pilhwa Lee

This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method…

Numerical Analysis · Mathematics 2022-12-26 Wietse M. Boon , Alessio Fumagalli , Anna Scotti

This paper is devoted to the stability analysis of a classical three-field formulation of Biot's consolidation model where the unknown variables are the displacements, fluid flux (Darcy velocity), and pore pressure. Specific…

Numerical Analysis · Mathematics 2018-06-21 Qingguo Hong , Johannes Kraus

In this paper we study the linear systems arising from discretized poroelasticity problems. We formulate one block preconditioner for the two-filed Biot model and several preconditioners for the classical three-filed Biot model under the…

Numerical Analysis · Mathematics 2020-07-15 Shuangshuang Chen , Qingguo Hong , Jinchao Xu , Kai Yang

In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the…

Numerical Analysis · Mathematics 2020-02-19 Michele Botti , Daniele A. Di Pietro , Olivier Le Maître , Pierre Sochala