TY - JOUR
T1 - Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations
AU - Alhammali , Azhar
AU - Peszynska , Malgorzata
AU - Shin , Choah
JO - International Journal of Numerical Analysis and Modeling
VL - 1
SP - 20
EP - 64
PY - 2024
DA - 2024/01
SN - 21
DO - http://doi.org/10.4208/ijnam2024-1002
UR - https://global-sci.org/intro/article_detail/ijnam/22328.html
KW - Parabolic variational inequality, nonlinear coupled system, mixed finite element
method, error estimates, biofilm–nutrient model, porous media.
AB - <p style="text-align: justify;">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.</p>