RESEARCH ARTICLE
Numerical analysis of a parabolic variational inequality system modeling biofilm growth at the porescale
Azhar Alhammali,
Malgorzata Peszynska,
Azhar Alhammali
Department of Mathematics, Oregon State University, Corvallis, Oregon
Search for more papers by this authorCorresponding Author
Malgorzata Peszynska
Department of Mathematics, Oregon State University, Corvallis, Oregon
Correspondence
Malgorzata Peszynska, Department of Mathematics, Oregon State University, Corvallis, OR.
Email: [email protected]
Search for more papers by this authorAzhar Alhammali,
Malgorzata Peszynska,
Azhar Alhammali
Department of Mathematics, Oregon State University, Corvallis, Oregon
Search for more papers by this authorCorresponding Author
Malgorzata Peszynska
Department of Mathematics, Oregon State University, Corvallis, Oregon
Correspondence
Malgorzata Peszynska, Department of Mathematics, Oregon State University, Corvallis, OR.
Email: [email protected]
Search for more papers by this authorFunding information Division of Mathematical Sciences, NSF DMS-1912938; NSF DMS-1522734; NSF-IRD plan 2019-20
Abstract
In this article, we consider a system of two coupled nonlinear diffusion–reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject to a pointwise constraint, thus the biofilm PDE is framed as a parabolic variational inequality. We derive rigorous error estimates for a finite element approximation to the coupled nonlinear system and confirm experimentally that the numerical approximation converges at the predicted rate. We also show simulations in which we track the free boundary in the domains which resemble the pore scale geometry and in which we test the different modeling assumptions.
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