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We focus on the numerical analysis of a polygonal discontinuous Galerkin scheme for the simulation of the exchange of fluid between a deformable saturated poroelastic structure and an adjacent free-flow channel. We specifically address wave…

Numerical Analysis · Mathematics 2025-02-03 Michele Botti , Ivan Fumagalli , Ilario Mazzieri

We study a decoupling iterative algorithm based on domain decomposition for the time-dependent nonlinear Stokes-Darcy model, in which different time steps can be used in the flow region and in the porous medium. The coupled system is…

Numerical Analysis · Mathematics 2020-07-06 Thi-Thao-Phuong Hoang , Hyesuk Lee

We study a new fully averaged poroelastic Kirchhoff plate model coupled with the flow of an incompressible, viscous fluid governed by the time-dependent Stokes equations. The fully averaged formulation offers several advantages over the…

Analysis of PDEs · Mathematics 2026-05-20 Felix Brandt , Sunčica Čanić , Andrew Scharf , Josip Tambača

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

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

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

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

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

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

We study the interaction between an incompressible, viscous, Newtonian fluid and a multilayered structure, which consists of a thin elastic layer and a thick poroelastic material. The thin layer is modeled using the linearly elastic Koiter…

Numerical Analysis · Mathematics 2013-08-22 Martina Bukac , Paolo Zunino , Ivan Yotov

We consider a chemotaxis-Navier-Stokes system modelling cellular swimming in fluid drops where an exchange of oxygen between the drop and its environment is taken into account. This phenomenon results in an inhomogeneous Robin-type boundary…

Analysis of PDEs · Mathematics 2019-09-30 Marcel Braukhoff , Bao Quoc Tang

A filtration system, comprising a Biot poroelastic solid coupled to an incompressible Stokes free-flow, is considered in 3D. Across the flat 2D interface, the Beavers-Joseph-Saffman coupling conditions are taken. In the inertial, linear,…

Analysis of PDEs · Mathematics 2024-03-18 George Avalos , Elena Gurvich , Justin T. Webster

We present a parallel time-stepping method for fluid-structure interactions. The interaction between the incompressible Navier-Stokes equations and a hyperelastic solid is formulated in a fully monolithic framework. Discretization in space…

Numerical Analysis · Mathematics 2022-01-19 Nils Margenberg , Thomas Richter

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

We prove the existence of martingale solutions to a stochastic fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the Navier-Stokes equations, through a deformable elastic tube modeled by…

Analysis of PDEs · Mathematics 2024-02-22 Krutika Tawri

This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…

Numerical Analysis · Mathematics 2022-11-09 Martina Bukac , Anyastassia Seboldt , Catalin Trenchea

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that…

Numerical Analysis · Mathematics 2023-08-31 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

Fluid flows in coupled systems consisting of a free-flow region and the adjacent porous medium appear in a variety of environmental settings and industrial applications. In many applications, fluid flow is non-parallel to the fluid-porous…

Analysis of PDEs · Mathematics 2021-04-07 Elissa Eggenweiler , Marco Discacciati , Iryna Rybak

We consider a parabolic-parabolic interface problem and construct a loosely coupled prediction-correction scheme based on the Robin-Robin splitting method analyzed in [J. Numer. Math., 31(1):59--77, 2023]. We show that the errors of the…

Numerical Analysis · Mathematics 2024-04-03 Erik Burman , Rebecca Durst , Miguel A. Fernández , Johnny Guzmán , Sijing Liu

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