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In this work, we introduce a novel algorithm for the Biot problem based on a Hybrid High-Order discretization of the mechanics and a Symmetric Weighted Interior Penalty discretization of the flow. The method has several assets, including,…

Numerical Analysis · Mathematics 2016-02-25 Daniele Boffi , Michele Botti , Daniele A. Di Pietro

In this paper, we propose a robust and efficient numerical framework for simulating multicomponent gas flow in poroelastic media, with a focus on preserving fundamental thermodynamic principles and ensuring computational reliability. The…

Numerical Analysis · Mathematics 2026-03-03 Huangxin Chen , Yuxiang Chen , Jisheng Kou , Shuyu Sun

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

Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…

Systems and Control · Electrical Eng. & Systems 2026-05-26 Antonio Carlucci

This work is concerned with the iterative solution of systems of quasi-static multiple-network poroelasticity (MPET) equations describing flow in elastic porous media that is permeated by single or multiple fluid networks. Here, the focus…

Numerical Analysis · Mathematics 2020-08-11 Qingguo Hong , Johannes Kraus , Maria Lymbery , Fadi Philo

We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux…

Numerical Analysis · Mathematics 2022-09-28 Wietse M. Boon

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…

Numerical Analysis · Mathematics 2023-06-07 Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

Magnetizable piezoelectric beams exhibit strong couplings between mechanical, electric, and magnetic fields, significantly affecting their high-frequency vibrational behavior. Ensuring exponential stability under boundary feedback…

Numerical Analysis · Mathematics 2026-04-07 Ahmet Kaan Aydin , Ahmet Ozkan Ozer , Jacob Walterman

In this paper, we propose a new multiphysics finite element method for a Biot model with secondary consolidation in soil dynamics. To better describe the processes of deformation and diffusion underlying in the original model, we…

Numerical Analysis · Mathematics 2022-04-08 Zhihao Ge , Wenlong He

In this work, semi-discrete and fully-discrete error estimates are derived for the Biot's consolidation model described using a three-field finite element formulation. The fields include displacements, total stress and pressure. The model…

Numerical Analysis · Mathematics 2020-08-05 Wenya Qi , Padmanabhan Seshaiyer , Junping Wang

We study the a priori error analysis of finite element methods for Biot's consolidation model. We consider a formulation which has the stress tensor, the fluid flux, the solid displacement, and the pore pressure as unknowns. Two mixed…

Numerical Analysis · Mathematics 2016-06-23 Jeonghun J. Lee

In this work we analyze an optimized artificial fixed-stress iteration scheme for the numerical approximation of the Biot system modelling fluid flow in deformable porous media. The iteration is based on a prescribed constant artificial…

Numerical Analysis · Mathematics 2017-05-24 M. Bause , F. A. Radu , U. Köcher

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

We study the fully mixed formulation of the Biot equations, which is characterized by a symmetric coupling between flow and deformation. This structure enables the use of stable mixed finite elements for each subproblem without a strong…

Numerical Analysis · Mathematics 2026-03-20 Fleurianne Bertrand , Jakub Wiktor Both , Tugay Dağlı

Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…

Numerical Analysis · Mathematics 2025-04-25 Michele Botti , Daniele Prada , Anna Scotti , Michele Visinoni

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress…

Numerical Analysis · Mathematics 2020-01-22 Kundan Kumar , Svetlana Kyas , Jan Nordbotten , Sergey Repin

In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional…

Numerical Analysis · Mathematics 2019-06-03 Ana Budiša , Xiaozhe Hu

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

The fixed-stress splitting scheme is a popular method for iteratively solving the Biot equations. The method successively solves the flow and mechanic subproblems while adding a stabilizing term to the flow equation, which includes a…

Numerical Analysis · Mathematics 2021-05-24 Erlend Storvik , Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

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