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This paper studies the thermo-poroelasticity model. By introducing an intermediate variable, we transform the original three-field model into a four-field model. Building upon this four-field model, we present both a coupled finite element…

Numerical Analysis · Mathematics 2025-07-23 Mingchao Cai , Jingzhi Li , Ziliang Li , Qiang Liu

Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…

Numerical Analysis · Mathematics 2016-06-22 Jeonghun J. Lee , Kent-Andre Mardal , Ragnar Winther

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 paper we consider a three-field formulation of the Biot model which has the displacement, the total pressure, and the pore pressure as unknowns. For parameter-robust stability analysis, we first show a priori estimates of the…

Numerical Analysis · Mathematics 2018-07-02 Jeonghun J. Lee

In this paper we propose a new finite element discretization for the two-field formulation of poroelasticity which uses the elastic displacement and the pore pressure as primary variables. The main goal is to develop a numerical method with…

Numerical Analysis · Mathematics 2023-08-08 Jeonghun J. Lee , Jacob Moore

We consider the Stokes-Darcy coupled problem, which models the interaction between free-flow and porous medium flow. By enforcing the normal flux continuity interface condition directly within the finite-element spaces, we establish unified…

Numerical Analysis · Mathematics 2025-07-22 Wietse M. Boon , Xiaozhe Hu , Xue Wang

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. The discretization is proved to be well-posed with respect to the physical and discretization parameters, and…

Numerical Analysis · Mathematics 2020-01-07 James H. Adler , Francisco J. Gaspar , Xiaozhe Hu , Peter Ohm , Carmen Rodrigo , Ludmil T. Zikatanov

This paper presents a scalable and robust solver for a cell-by-cell poroelasticity model, describing the mechanical interactions between brain cells embedded in extracellular space. Explicitly representing the complex cellular shapes, the…

Numerical Analysis · Mathematics 2026-03-11 Marius Causemann , Miroslav Kuchta

In this paper, we propose a new finite element solution approach to the multi-compartmental Darcy equations describing flow and interactions in a porous medium with multiple fluid compartments. We introduce a new numerical formulation and a…

Numerical Analysis · Mathematics 2020-03-24 Eleonora Piersanti , Marie E. Rognes , Kent-Andre Mardal

We discuss the construction of robust preconditioners for finite element approximations of Biot's consolidation model in poroelasticity. More precisely, we study finite element methods based on generalizations of the Hellinger-Reissner…

Numerical Analysis · Mathematics 2017-03-24 Trygve Baerland , Jeonghun J. Lee , Kent-Andre Mardal , Ragnar Winther

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

The parameters in the governing system of partial differential equations of multicompartmental poroelastic models typically vary over several orders of magnitude making its stable discretization and efficient solution a challenging task. In…

Numerical Analysis · Mathematics 2018-06-12 Qinggou Hong , Johannes Kraus , Maria Lymbery , Fadi Philo

The flow of incompressible fluids through porous media plays a crucial role in many technological applications such as enhanced oil recovery and geological carbon-dioxide sequestration. The flow within numerous natural and synthetic porous…

Computational Engineering, Finance, and Science · Computer Science 2018-05-23 S. H. S. Joodat , K. B. Nakshatrala , R. Ballarini

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

This paper concerns with finite element approximations of a quasi-static poroelasticity model in displacement-pressure formulation which describes the dynamics of poro-elastic materials under an applied mechanical force on the boundary. To…

Numerical Analysis · Mathematics 2014-12-01 Xiaobing Feng , Zhihao Ge , Yukun Li

In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…

Numerical Analysis · Mathematics 2026-02-24 Zhihao Ge , Wenshuai Hu

We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…

Numerical Analysis · Mathematics 2025-09-25 Sabit Mahmood Khan , Yashar Mehmani

We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…

Numerical Analysis · Mathematics 2023-07-06 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

Linear poroelasticity models have a number of important applications in biology and geophysics. In particular, Biot's consolidation model is a well-known model that describes the coupled interaction between the linear response of a porous…

Numerical Analysis · Mathematics 2020-03-17 Arbaz Khan , Catherine E. Powell

In this paper, we propose a multiphysics finite element method for a nonlinear poroelasticity model. To better describe the processes of deformation and diffusion, we firstly reformulate the nonlinear fluid-solid coupling problem into a…

Numerical Analysis · Mathematics 2021-12-28 Zhihao Ge , Wenlong He
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