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arXiv · 1908.09778

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

Nitesh Verma·Bryan Gomez-Vargas·Luis Miguel De Oliveira Vilaca·Sarvesh Kumar·Ricardo Ruiz-Baier
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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 rigorously 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.

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Nitesh Verma, Bryan Gomez-Vargas, Luis Miguel De Oliveira Vilaca, Sarvesh Kumar, Ricardo Ruiz-Baier. 2019-08-26. Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media. https://doi.org/10.1080/00036811.2021.1877677

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