Analysis of a finite-volume scheme for a single-species biofilm model

DOI10.1016/j.apnum.2022.12.002arXiv2110.14933MaRDI QIDQ6101762

Christoph Helmer, Ansgar Jüngel, Antoine Zurek

Publication date: 20 June 2023

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.14933

zbMATH Keywords

finite volumesbiofilm growthtwo-point flux approximationconvergence of the schemeentropy variable

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical analysis (65-XX) Parabolic equations and parabolic systems (35Kxx) Physiological, cellular and medical topics (92Cxx)

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Existence analysis for a reaction-diffusion Cahn-Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth

Cites Work

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• Analysis of a degenerate biofilm model with a nutrient taxis term
• Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects
• Finite volume approximation for an immiscible two-phase flow in porous media with discontinuous capillary pressure
• Time-discretization of a degenerate reaction-diffusion equation arising in biofilm modeling
• A mixed-culture biofilm model with cross-diffusion
• Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids
• Existence and longtime behavior of a biofilm model
• Convergence of a finite volume scheme for nonlinear degenerate parabolic equations
• Mathematical modeling of biofilm development
• Time adaptive numerical solution of a highly degenerate diffusion-reaction biofilm model based on regularisation
• Modeling of biocide action against biofilm
• A fluid dynamics model of the growth of phototrophic biofilms
• A nonlinear time compactness result and applications to discretization of degenerate parabolic-elliptic PDEs
• A New Deterministic Spatio-Temporal Continuum Model for Biofilm Development
• Entropy Methods for Diffusive Partial Differential Equations
• On discrete functional inequalities for some finite volume schemes
• Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis
• Time adaptive numerical solution of a highly non-linear degenerate cross-diffusion system arising in multi-species biofilm modelling
• Convergence of a finite-volume scheme for a degenerate-singular cross-diffusion system for biofilms
• Optimized Overlapping DDFV Schwarz Algorithms
• Numerical Solution of a Degenerate, Diffusion Reaction Based Biofilm Growth Model on Structured Non-Orthogonal Grids
• Finite‐volume scheme for a degenerate cross‐diffusion model motivated from ion transport
• Analysis of a Degenerate and Singular Volume-Filling Cross-Diffusion System Modeling Biofilm Growth