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Volume 21, Issue 1
Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations

Azhar Alhammali, Malgorzata Peszynska & Choah Shin

DOI: 10.4208/ijnam2024-1002

Int. J. Numer. Anal. Mod., 21 (2024), pp. 20-64.

Published online: 2024-01

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  • 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.

  • Keywords

Parabolic variational inequality, nonlinear coupled system, mixed finite element method, error estimates, biofilm–nutrient model, porous media.

  • AMS Subject Headings

35R35, 49J40, 65M60

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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} }
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 -

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.

Alhammali , AzharPeszynska , Malgorzata and Shin , Choah. (2024). Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations. International Journal of Numerical Analysis and Modeling. 21 (1). 20-64. doi:10.4208/ijnam2024-1002
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