Condition number for finite element discretisation of nonlocal PDE systems with applications to biology

2025/08/13 by Adebayo, Olusegun E., Eftimie, Raluca, Trucu, Dumitru
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2508.09781

Abstract

In this work, we investigate the condition number for a system of coupled non-local reaction-diffusion-advection equations developed in the context of modelling normal and abnormal wound healing. Following a finite element discretisation of the coupled non-local system, we establish bounds for this condition number. We further discuss how model parameter choices affect the conditioning of the system. Finally, we discuss how the step size of the chosen time-stepping scheme and the spatial grid size of the finite element methods affect the bound for the condition number, while also suggesting possible parameter ranges that could keep the model well conditioned.

Citations

• Numerical Approaches for non-local Transport-Dominated PDE Models with Applications to Biology
• Error analysis for finite element operator learning methods for solving parametric second-order elliptic PDEs
• Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
• Nonlocal and local models for taxis in cell migration: a rigorous limit\n procedure
• Multiscale Modelling of Fibres Dynamics and Cell Adhesion within Moving\n Boundary Cancer Invasion
• Nonstandard local discontinuous Galerkin methods for fully nonlinear second order elliptic and parabolic equations in high dimensions

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