@Article{IJNAM-21-20,
author = {Alhammali , AzharPeszynska , Malgorzata and Shin , Choah},
title = {Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2024},
volume = {21},
number = {1},
pages = {20--64},
abstract = {<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>},
issn = {2617-8710},
doi = {https://doi.org/10.4208/ijnam2024-1002},
url = {http://global-sci.org/intro/article_detail/ijnam/22328.html}
}