Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

 

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Autoři: Verma, Nitesh, Gómez Vargas, Bryan Andrés, De Oliveira Vilaca, Luis Miguel, Kumar, Sarvesh, Ruiz Baier, Ricardo
Médium: artículo original
Datum vydání:2021
Popis: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 investigate the well-posedness of the nonlinear set of equations using fixed-point theory, Fredholm’s alternative, a priori estimates, and compactness arguments. We also propose a mixed finite element method and demonstrate the stability of the scheme. Error estimates are derived in suitable norms, and numerical experiments are conducted to illustrate the mechano-chemical coupling and to verify the theoretical rates of convergence.
Země:Kérwá
Instituce:Universidad de Costa Rica
Repositorio:Kérwá
Jazyk:Inglés
OAI Identifier:oai:kerwa.ucr.ac.cr:10669/86459
On-line přístup:https://www.tandfonline.com/journals/gapa20
https://hdl.handle.net/10669/86459
Klíčové slovo:Biot equations
Reaction-diffusion
Mixed finite element scheme
Well-posedness and stability
Numerical experiments and error estimates