Numerical Analysis of a Mixed Finite Element Approximation of a Coupled System Modeling Biofilm Growth in Porous Media with Simulations

IF 1.3 4区数学 Q1 MATHEMATICS

International Journal of Numerical Analysis and Modeling Pub Date : 2024-01-01 DOI:10.4208/ijnam2024-1002

Azhar Alhammali,Malgorzata Peszynska, Choah Shin

引用次数: 0

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.

查看原文本刊更多论文

模拟多孔介质中生物膜生长的耦合系统的混合有限元近似数值分析

本文考虑对模拟多孔介质中孔隙尺度生物膜生长和养分利用的非线性抛物平流-扩散-反应变（不）等式耦合系统进行混合有限元近似。我们研究了该离散系统的拟合优度，并得出了一阶最优误差估计。我们的理论估计将 Arbogast 等人 1997 年[4]关于标量退化抛物线问题的工作扩展到变分问题；我们还将其应用于一个系统。我们还通过对现实场景的模拟来验证我们的理论收敛结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal of Numerical Analysis and Modeling 数学-数学

CiteScore

2.10

自引率

9.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal is directed to the broad spectrum of researchers in numerical methods throughout science and engineering, and publishes high quality original papers in all fields of numerical analysis and mathematical modeling including: numerical differential equations, scientific computing, linear algebra, control, optimization, and related areas of engineering and scientific applications. The journal welcomes the contribution of original developments of numerical methods, mathematical analysis leading to better understanding of the existing algorithms, and applications of numerical techniques to real engineering and scientific problems. Rigorous studies of the convergence of algorithms, their accuracy and stability, and their computational complexity are appropriate for this journal. Papers addressing new numerical algorithms and techniques, demonstrating the potential of some novel ideas, describing experiments involving new models and simulations for practical problems are also suitable topics for the journal. The journal welcomes survey articles which summarize state of art knowledge and present open problems of particular numerical techniques and mathematical models.