- Journal Home
- Volume 22 - 2025
- Volume 21 - 2024
- Volume 20 - 2023
- Volume 19 - 2022
- Volume 18 - 2021
- Volume 17 - 2020
- Volume 16 - 2019
- Volume 15 - 2018
- Volume 14 - 2017
- Volume 13 - 2016
- Volume 12 - 2015
- Volume 11 - 2014
- Volume 10 - 2013
- Volume 9 - 2012
- Volume 8 - 2011
- Volume 7 - 2010
- Volume 6 - 2009
- Volume 5 - 2008
- Volume 4 - 2007
- Volume 3 - 2006
- Volume 2 - 2005
- Volume 1 - 2004
Int. J. Numer. Anal. Mod., 21 (2024), pp. 20-64.
Published online: 2024-01
Cited by
- BibTex
- RIS
- TXT
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.
}, issn = {2617-8710}, doi = {https://doi.org/10.4208/ijnam2024-1002}, url = {http://global-sci.org/intro/article_detail/ijnam/22328.html} }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.