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In this paper we propose a novel coupled poroelasticity-diffusion model for the formation of extracellular oedema and infectious myocarditis valid in large deformations, manifested as an interaction between interstitial flow and the…

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 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

We develop a family of mixed finite element methods for a model of nonlinear poroelasticity where, thanks to a rewriting of the constitutive equations, the permeability depends on the total poroelastic stress and on the fluid pressure and…

Numerical Analysis · Mathematics 2025-02-25 Arbaz Khan , Bishnu P. Lamichhane , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

In this paper a new primal-dual mixed finite element method is introduced, aimed to model multiscale problems with several geometric subregions in the domain of interest. In each of these regions porous media fluid flow takes place, but…

Numerical Analysis · Mathematics 2020-08-21 Fernando A Morales

In this paper, we propose a numerical method for computing solutions to Biot's fully dynamic model of incompressible saturated porous media [Biot;1956]. Our spatial discretization scheme is based on the three-field formulation (u-w-p) and…

Numerical Analysis · Mathematics 2015-06-24 Zahrasadat Lotfian , Mettupalayam Sivaselvan

In this work, we present and analyze a fully-mixed finite element scheme for the dynamic poroelasticity problem in the low-frequency regime. We write the problem as a four-field, first-order, hyperbolic system of equations where the…

Numerical Analysis · Mathematics 2025-12-12 Stefano Bonetti , Michele Botti , Patrick Vega

The focus of this contribution is the numerical treatment of interface coupled problems concerning the interaction of incompressible fluid flow and permeable, elastic structures. The main emphasis is on extending the range of applicability…

Computational Engineering, Finance, and Science · Computer Science 2019-05-01 Christoph Ager , Benedikt Schott , Magnus Winter , Wolfgang A. Wall

In this paper, we consider the complex flows when all three regimes pre-Darcy, Darcy and post-Darcy may be present in different portions of a same domain. We unify all three flow regimes under mathematics formulation. We describe the flow…

Numerical Analysis · Mathematics 2021-06-24 John Cummings , Matthew Hamilton , Thinh Kieu

We present a numerical method to model the dynamics of inextensible biomembranes in a quasi-Newtonian incompressible flow, which better describes hemorheology in the small vasculature. We consider a level set model for the fluid-membrane…

General Mathematics · Mathematics 2023-05-30 Aymen Laadhari , Ahmad Deeb

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 modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…

Analysis of PDEs · Mathematics 2022-01-03 Mina Karimi , Mehrdad Massoudi , Noel Walkington , Matteo Pozzi , Kaushik Dayal

We present a stabilised finite element method for modelling proton transport in tissue, incorporating both inelastic energy loss and elastic angular scattering. A key innovation is a positivity-preserving formulation that guarantees…

Numerical Analysis · Mathematics 2025-06-03 Ben S. Ashby , Abdalaziz Hamdan , Tristan Pryer

The finite element simulation of dynamic wetting phenomena, requiring the computation of flow in a domain confined by intersecting a liquid-fluid free surface and a liquid-solid interface, with the three-phase contact line moving across the…

Computational Physics · Physics 2012-02-20 J. E. Sprittles , Y. D. Shikhmurzaev

We consider implementational aspects of the mixed finite element method for a special class of nonlinear problems. We establish the equivalence of the hybridized formulation of the mixed finite element method to a nonconforming finite…

Numerical Analysis · Mathematics 2016-10-19 Peter Knabner , Gerhard Summ

This article considers a model problem of elastoplasticity with linearly kinematic hardening and presents hp-finite element discretizations of two equivalent weak formulations each having their respective advantages. A mixed variational…

Numerical Analysis · Mathematics 2026-05-12 Patrick Bammer , Lothar Banz , Miriam Schönauer , Andreas Schröder

Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…

Applied Physics · Physics 2019-10-22 Elias Karabelas , Gundolf Haase , Gernot Plank , Christoph M. Augustin

We consider a sharp interface formulation for an anisotropic multi-phase Mullins-Sekerka problem with kinetic undercooling. The flow is characterized by a cluster of surfaces evolving such that the total surface energy plus a weighted sum…

Numerical Analysis · Mathematics 2026-02-23 Tokuhiro Eto , Harald Garcke , Robert Nürnberg

In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velocity and pressure of the fluid. Additionally, the points…

Numerical Analysis · Mathematics 2019-05-01 Kyle Dunn , Roger Lui , Marcus Sarkis

A finite element method with mass-lumping and flux upwinding, is formulated for solving the immiscible two-phase flow problem in porous media. The method approximates directly the wetting phase pressure and saturation, which are the primary…

Numerical Analysis · Mathematics 2020-01-27 Girault Vivette , Riviere Beatrice , Cappanera Loic