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Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem
(2020)
In this paper we introduce a new formulation for the stationary poroelasticity equations written using the rotation vector and the total fluid-solid pressure as additional unknowns, and we also write an extension to the ...
Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media
(2021)
We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We ...
Stability of a second-order method for phase change in porous media flow
(2018)
We analyse the stability of a second-order finite element scheme for the primal formulation of a Brinkman-Boussinesq model where the solidification process influences the drag and the viscosity. The problem is written in ...
New mixed finite element methods for natural convection with phase-change in porous media
(2019)
This article is concerned with the mathematical and numerical analysis of a steady phase change problem for non-isothermal incompressible viscous flow. The system is formulated in terms of pseudostress, strain rate and ...
Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion
(2023)
We present a new stress/total-pressure formulation for poroelasticity that incorporates the coupling with steady nonlinear diffusion modified by stress. This nonlinear problem is written in mixed-primal form, which combines ...
Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema
(2022-07-22)
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 ...
A posteriori error analysis of mixed finite element methods for stress-assisted diffusion problems
(2022)
We develop the a posteriori error analysis for mixed-primal and fully-mixed finite element methods approximating the stress-assisted diffusion of solutes in elastic materials. The systems are formulated in terms of stress, ...
Formulation and analysis of fully-mixed methods for stress-assisted diffusion problems
(2019-03)
This paper is devoted to the mathematical and numerical analysis of a mixed-mixed PDE system describing the stress-assisted diffusion of a solute into an elastic material. The equations of elastostatics are written in mixed ...
Stability and finite element approximation of phase change models for natural convection in porous media
(2019-11)
In this paper we study a phase change problem for non-isothermal incompressible viscous flows. The underlying continuum is modelled as a viscous Newtonian fluid where the change of phase is either encoded in the viscosity ...
Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems
(2018)
We analyse the solvability of a static coupled system of PDEs describing the diffusion of a solute into an elastic material, where the process is affected by the stresses exerted in the solid. The problem is formulated in ...