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Related papers: A mixed elasticity formulation for fluid-poroelast…

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We propose four-field and five-field Hu--Washizu-type mixed formulations for nonlinear poroelasticity -- a coupled fluid diffusion and solid deformation process -- considering that the permeability depends on a linear combination between…

Numerical Analysis · Mathematics 2025-02-20 Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

A mixed finite element method for the Navier-Stokes equations is introduced in which the stress is a primary variable. The variational formulation retains the mathematical structure of the Navier-Stokes equations and the classical theory…

Numerical Analysis · Mathematics 2016-03-31 Jason S. Howell , Noel J. Walkington

In this paper, we study a nonlinear fluid-structure interaction problem driven by a multiplicative, white-in-time noise. The problem consists of the Navier-Stokes equations describing the flow of an incompressible, viscous fluid in a 2D…

Analysis of PDEs · Mathematics 2024-02-14 Krutika Tawri

We present projection-based mixed finite element methods for the solution of the unsteady Brinkman equations for incompressible single-phase flow with fixed in space porous solid inclusions. At each time step the method requires the…

Numerical Analysis · Mathematics 2025-09-24 Costanza Aricò , Rainer Helmig , Ivan Yotov

The goal of this paper is to develop and analyze some fully discrete finite element methods for a displacement-pressure model modeling swelling dynamics of polymer gels under mechanical constraints. In the model, the swelling dynamics is…

Numerical Analysis · Mathematics 2009-03-25 Xiaobing Feng , Yinnian He

In this brief note, we introduce a non-symmetric mixed finite element formulation for Brinkman equations written in terms of velocity, vorticity and pressure with non-constant viscosity. The analysis is performed by the classical…

Numerical Analysis · Mathematics 2019-05-07 Verónica Anaya , Bryan Gómez-Vargas , David Mora , Ricardo Ruiz-Baier

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes…

Analysis of PDEs · Mathematics 2016-02-17 C. Grandmont , M. Hillairet

In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We…

Numerical Analysis · Computer Science 2010-04-12 K. B. Nakshatrala , K. R. Rajagopal

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 two and three dimensional domains, we analyze mixed finite element methods for a velocity-pressure-pseudostress formulation of the Stokes eigenvalue problem. The methods consist in two schemes: the velocity and pressure are approximated…

Numerical Analysis · Mathematics 2021-03-09 Felipe Lepe , Gonzalo Rivera , Jesus Vellojin

The work investigates a model that combines a convection-diffusion-reaction equation for solute concentration with an unsteady Darcy-Brinkman equation for the flow field, including the Kortweg stress. Additionally, the flow field…

Analysis of PDEs · Mathematics 2024-06-11 Sahil Kundu , Surya Narayan Maharana , Manoranjan Mishra

The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation and is so simple such that both velocity and pressure are…

Numerical Analysis · Mathematics 2016-10-19 Lin Mu , Xiu Ye

We propose mixed finite element methods for Cosserat materials that use suitable quadrature rules to eliminate the Cauchy and coupled stress variables locally. The reduced system consists of only the displacement and rotation variables.…

Numerical Analysis · Mathematics 2025-11-11 Wietse M. Boon , Alessio Fumagalli , Jan M. Nordbotten , Ivan Yotov

A homogenised model is developed to describe the interaction between aligned strings and an incompressible, viscous, Newtonian fluid. In the case of many strings, the ratio of string separation to domain width gives a small parameter which…

Fluid Dynamics · Physics 2022-02-15 A. Kent , S. L. Waters , J. Oliver , S. J. Chapman

This paper explores the application of the multiscale finite element method (MsFEM) to address steady-state Stokes-Darcy problems with BJS interface conditions in highly heterogeneous porous media. We assume the existence of multiscale…

Numerical Analysis · Mathematics 2024-01-09 Yachen Hong , Wenhan Zhang , Lina Zhao , Haibiao Zheng

We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…

Numerical Analysis · Mathematics 2025-10-07 Arbaz Khan , David Mora , Ricardo Ruíz-Baier , Jesus Vellojin

We present an implementation of a fully variational formulation of an immersed method for fluid-structure interaction problems based on the finite element method. While typical implementation of immersed methods are characterized by the use…

Numerical Analysis · Mathematics 2015-04-10 Saswati Roy , Luca Heltai , Francesco Costanzo

We present a theoretical and computational model for the behavior of a porous solid undergoing two interdependent processes, the finite deformation of a solid and species migration through the solid, which are distinct in bulk and on…

Soft Condensed Matter · Physics 2023-05-16 Jaemin Kim , Ida Ang , Francesco Ballarin , Chung-Yuen Hui , Nikolaos Bouklas

We consider the quasi-static Biot's consolidation model in a three-field formulation with the three unknown physical quantities of interest being the displacement $\boldsymbol{u}$ of the solid matrix, the seepage velocity $\boldsymbol{v}$…

Numerical Analysis · Mathematics 2021-07-07 Johannes Kraus , Philip L. Lederer , Maria Lymbery , Joachim Schöberl

Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…

Numerical Analysis · Mathematics 2017-11-28 Eldar Khattatov , Ivan Yotov