Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations
Year: 2024
Author: Azhar Alhammali, Malgorzata Peszynska, Choah Shin
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 20–64
Abstract
In this paper, we consider mixed finite element approximation of a coupled system of nonlinear parabolic advection-diffusion-reaction variational (in)equalities modeling biofilm growth and nutrient utilization in porous media at pore-scale. We study well-posedness of the discrete system and derive an optimal error estimate of first order. Our theoretical estimates extend the work on a scalar degenerate parabolic problem by Arbogast et al, 1997 [4] to a variational inequality; we also apply it to a system. We also verify our theoretical convergence results with simulations of realistic scenarios.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ijnam2024-1002
International Journal of Numerical Analysis and Modeling, Vol. 21 (2024), Iss. 1 : pp. 20–64
Published online: 2024-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 45
Keywords: Parabolic variational inequality nonlinear coupled system mixed finite element method error estimates biofilm–nutrient model porous media.