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Related papers: Fully-Mixed Virtual Element Method for the Biot Pr…

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In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the…

Numerical Analysis · Mathematics 2025-10-23 Sarvesh Kumar , Utkarsh Rajput , Ricardo Ruiz-Baier

The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On…

Soft Condensed Matter · Physics 2019-02-15 Pascale Royer , Pierre Recho , Claude Verdier

We introduce and analyze a partially augmented fully-mixed formulation and a mixed finite element method for the coupled problem arising in the interaction between a free fluid and a poroelastic medium. The flows in the free fluid and…

Numerical Analysis · Mathematics 2023-05-02 Tongtong Li , Sergio Caucao , Ivan Yotov

We present a hybrid mimetic finite-difference and virtual element formulation for coupled single-phase poromechanics on unstructured meshes. The key advantage of the scheme is that it is convergent on complex meshes containing highly…

Numerical Analysis · Mathematics 2021-06-09 Andrea Borio , François Hamon , Nicola Castelletto , Joshua A. White , Randolph R. Settgast

In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisfy an inf-sup condition uniformly with respect to the…

Numerical Analysis · Mathematics 2018-08-15 Carmen Rodrigo , Xiaozhe Hu , Peter Ohm , James H. Adler , Francisco J. Gaspar , Ludmil Zikatanov

In conventional formulations of poroelasticity, when the porosity approaches zero or vanishes in some parts of the poroelastic domain, if only temporarily, the governing equations degenerate to those for the solid phase thereby inhibiting a…

Fluid Dynamics · Physics 2025-10-29 Mohammad Jannesari , Beatrice Ghitti , Bruce J. Gluckman , Francesco Costanzo

We present the Neural Approximated Virtual Element Method to numerically solve elasticity problems. This hybrid technique combines classical concepts from the Finite Element Method and the Virtual Element Method with recent advances in deep…

Numerical Analysis · Mathematics 2025-07-09 Stefano Berrone , Moreno Pintore , Gioana Teora

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

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

In this work, we present a new stabilization method aimed at removing spurious oscillations in the pressure approximation of Biot's model for poroelasticity with low permeabilities and/or small time steps. We consider different…

Numerical Analysis · Mathematics 2024-07-30 Álvaro Pé de la Riva , Francisco J. Gaspar , Xiaozhe Hu , James Adler , Carmen Rodrigo , Ludmil Zikatanov

The paper deals with modelling fluid saturated porous media subject to large deformation. An Eulerian incremental formulation is derived using the problem imposed in the spatial configuration in terms of the equilibrium equation and the…

Numerical Analysis · Mathematics 2018-01-17 Eduard Rohan , Vladimír Lukeš

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

An alternative to the fully implicit or monolithic methods used for the solution of the coupling of fluid flow and deformation in porous media is a sequential approach in which the fully coupled system is broken into subproblems (flow and…

Numerical Analysis · Mathematics 2025-12-23 Xiaozhe Hu , Francisco J. Gaspar , Carmen Rodrigo

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

The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing…

Numerical Analysis · Mathematics 2023-10-06 L. L. Yaw

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…

Numerical Analysis · Mathematics 2023-06-27 Bryan Gomez-Vargas , Kent-Andre Mardal , Ricardo Ruiz-Baier , Vegard Vinje

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 introduce and analyse a fully-mixed formulation for the coupled problem arising in the interaction between a free fluid and a poroelastic medium.The flows in the free fluid and poroelastic regions are governed by the Navier-Stokes and…

Numerical Analysis · Mathematics 2025-12-16 Sergio Caucao , Aashi Dalal , Ivan Yotov

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

Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…

Numerical Analysis · Mathematics 2017-07-18 Wietse M. Boon , Jan M. Nordbotten , Ivan Yotov