A gradient Discretisation Method For Anisotropic Reaction Diffusion Models with applications to the dynamics of brain tumours

TL;DR

This paper introduces a gradient discretisation method (GDM) for anisotropic reaction-diffusion models, with applications to brain tumour dynamics, providing convergence analysis and exploring various numerical schemes.

Contribution

It develops a unified GDM framework for anisotropic models, analyzing convergence and existence of solutions, and compares multiple numerical discretisation schemes.

Findings

GDM ensures convergence for anisotropic reaction-diffusion models.

Numerical schemes like HMM and Crouzeix--Raviart are effective.

Application to brain tumour dynamics demonstrates practical utility.

Abstract

A gradient discretisation method (GDM), Gradient schemes, Convergence analysis, Existence of weak solutions, Anisotropic reaction diffusion models, Dirichlet and Neumann boundary conditions, Non conforming finite element methods, Finite volume schemes, Hybrid mixed mimetic (HMM) method, Crouzeix--Raviart scheme, Brain tumour dynamics, Fractional anisotropy.