Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media. Issue 14 (22nd September 2022)

• Record Type: Journal Article
• Authors: Verma, Nitesh; Gómez-Vargas, Bryan; De Oliveira Vilaca, Luis Miguel; Kumar, Sarvesh; Ruiz-Baier, Ricardo
• Is Part Of: Applicable analysis. Volume 101:Issue 14(2022)
• Page Start: 4914
• Page End: 4941
• Publication Date: 2022-09-22
• Subjects: Biot equations -- reaction-diffusion -- mixed finite element scheme -- well-posedness and stability -- numerical experiments and error estimates; 65M60 -- 74F10 -- 35K57 -- 74L15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2021.1877677
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: 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.