Listar Matemática por autor "90dc0271-8792-4e56-a119-d19c7235d0b8"
Mostrando ítems 1-13 de 13
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A posteriori error analysis of mixed finite element methods for stress-assisted diffusion problems
Gatica Pérez, Gabriel Nibaldo; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo (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, ... -
Analysis and mixed-primal finite element discretisations for stress-assisted diffusion problems
Gatica Pérez, Gabriel Nibaldo; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo (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 ... -
Finite Element Methods for Large-Strain Poroelasticity/Chemotaxis Models Simulating the Formation of Myocardial Oedema
Barnafi Wittwer, Nicolás Alejandro; Gómez Vargas, Bryan Andrés; Lourenço, Wesley De Jesus; Reis, Ruy Freitas; Rocha, Bernardo Martins; Lobosco, Marcelo; Ruiz Baier, Ricardo; Weber dos Santos, Rodrigo (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 ... -
Formulation and analysis of fully-mixed methods for stress-assisted diffusion problems
Gatica Pérez, Gabriel Nibaldo; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo (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 ... -
Incorporating variable viscosity in vorticity-based formulations for Brinkman equations
Anaya Domínguez, Verónica; Gómez Vargas, Bryan Andrés; Mora Herrera, David; Ruiz Baier, Ricardo (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 ... -
New mixed finite element methods for natural convection with phase-change in porous media
Álvarez Guadamuz, Mario Andrés; Gatica Pérez, Gabriel Nibaldo; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo (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 ... -
Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem
Anaya Domínguez, Verónica; De Wijn, Zoa; Gómez Vargas, Bryan Andrés; Mora Herrera, David; Ruiz Baier, Ricardo (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 ... -
Stability analysis for a new model of multi-species convection-diffusion-reaction in poroelastic tissue
De Oliveira Vilaca, Luis Miguel; Gómez Vargas, Bryan Andrés; Kumar, Sarvesh; Ruiz Baier, Ricardo; Verma, Nitesh (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 ... -
Stability and finite element approximation of phase change models for natural convection in porous media
Woodfield, James; Álvarez Guadamuz, Mario Andrés; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo (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 ... -
Stability of a second-order method for phase change in porous media flow
Álvarez Guadamuz, Mario Andrés; Gómez Vargas, Bryan Andrés; Ruiz Baier, Ricardo; Woodfield, James (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 ... -
Twofold Saddle-Point Formulation of Biot Poroelasticity with Stress-Dependent Diffusion
Gómez Vargas, Bryan Andrés; Mardal, Kent André; Ruiz Baier, Ricardo; Vinje, Vegard (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 ... -
Velocity‑vorticity‑pressure formulation for the Oseen problem with variable viscosity
Anaya Domínguez, Verónica; Caraballo, Rubén; Gómez Vargas, Bryan Andrés; Mora Herrera, David; Ruiz Baier, Ricardo (2021)We propose and analyse an augmented mixed finite element method for the Oseen equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and homogeneous Dirichlet boundary condition for the ... -
Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media
Verma, Nitesh; Gómez Vargas, Bryan Andrés; De Oliveira Vilaca, Luis Miguel; Kumar, Sarvesh; Ruiz Baier, Ricardo (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 ...