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In this paper, we present and analyze a new mixed finite element formulation of a general family of quasi-static multiple-network poroelasticity (MPET) equations. The MPET equations describe flow and deformation in an elastic porous medium…

Numerical Analysis · Mathematics 2018-04-23 Jeonghun J. Lee , Eleonora Piersanti , Kent-Andre Mardal , Marie E. Rognes

Cellular morphodynamics requires solving systems of coupled partial differential equations on moving bulk and surface domains, where advection-dominant transport, structure preservation, and severe mesh distortions make robust simulation…

Numerical Analysis · Mathematics 2026-01-12 Alessandro Contri , André Massing , Padmini Rangamani

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

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 ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…

Numerical Analysis · Mathematics 2026-04-15 Xianping Li , Woinshet D. Mergia , Kailash C. Patidar

We develop non-overlapping domain decomposition methods for the Biot system of poroelasticity in a mixed form. The solid deformation is modeled with a mixed three-field formulation with weak stress symmetry. The fluid flow is modeled with a…

Numerical Analysis · Mathematics 2021-08-04 Manu Jayadharan , Eldar Khattatov , Ivan Yotov

We propose a new full discretization of the Biot's equations in poroelasticity. The construction is driven by the inf-sup theory, which we recently developed. It builds upon the four-field formulation of the equations obtained by…

Numerical Analysis · Mathematics 2024-07-04 C. Kreuzer , P. Zanotti

We consider a multiphysics model for the flow of Newtonian fluid coupled with Biot consolidation equations through an interface, and incorporating total pressure as an unknown in the poroelastic region. A new mixed-primal finite element…

Numerical Analysis · Mathematics 2023-06-27 Ricardo Ruiz-Baier , Matteo Taffetani , Hans D. Westermeyer , Ivan Yotov

A diffusion interface two-phase magnetohydrodynamic model has been used for matched densities in our previous work [1,2], which may limit the applications of the model. In this work, we derive a thermodynamically consistent diffuse…

Numerical Analysis · Mathematics 2024-03-13 Ke Zhang

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 paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…

Numerical Analysis · Mathematics 2017-07-12 Sébastien Court , Michel Fournié

In this paper a time dependent Stokes problem that is motivated by a standard sharp interface model for the fluid dynamics of two-phase flows is studied. This Stokes interface problem has discontinuous density and viscosity coefficients and…

Numerical Analysis · Mathematics 2018-07-12 Igor Voulis , Arnold Reusken

We resolve the issue of uniqueness of weak solutions for linear, inertial fluid-poroelastic-structure coupled dynamics. The model comprises a 3D Biot poroelastic system coupled to a 3D incompressible Stokes flow via a 2D interface, where…

Analysis of PDEs · Mathematics 2025-02-12 George Avalos , Justin T. Webster

Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a finite element setting is proposed to better investigate this…

Fluid Dynamics · Physics 2017-11-28 Julien Bruchon , Yujie Liu , Nicolas Moulin

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

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…

Numerical Analysis · Mathematics 2025-04-02 Jialin Xie , Xiaodi Zhang

We present a novel artificial diffusion method to circumvent the instabilities associated with the standard finite element approximation of convection-diffusion equations. Motivated by the micromorphic approach, we introduce an auxiliary…

Numerical Analysis · Mathematics 2025-06-19 Soheil Firooz , B. Daya Reddy , Paul Steinmann

Biot's theory provides a framework for computing seismic wavefields in fluid saturated porous media. Here we implement a velocity-stress staggered grid 2D finite difference algorithm to model the wave-propagation in poroelastic media. The…

Geophysics · Physics 2019-07-29 Janaki Vamaraju , Mrinal K. Sen
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