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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 ...
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 ...
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 ...
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 ...
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 ...
Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue
(2020)
We perform the linear stability analysis of a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and ...
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 ...
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 ...
Incorporating variable viscosity in vorticity-based formulations for Brinkman equations
Intégration de la viscosité variable dans des formulations en tourbillon pour les équations de Brinkman
(2019-06)
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 ...