General Error Estimates of Non Conforming Approximation of System of Reaction-Diffusion Equations

TL;DR

This paper develops a general error estimation framework for non-conforming numerical schemes approximating reaction-diffusion systems, applicable broadly and validated through finite volume method results.

Contribution

It introduces a comprehensive error estimate for SRDEs using GDM, applicable to various schemes including non-conforming methods, with proven existence and uniqueness.

Findings

Error estimates valid for all conforming and non-conforming schemes within GDM

Existence and uniqueness of approximate solutions established

Numerical validation using finite volume method

Abstract

This paper aims to establish a first general error estimate for numerical approximations of the system of reaction-diffusion equations (SRDEs), using reasonable regularity assumptions on the exact solutions. We employ the gradient discretisation method (GDM) to discretise the system and prove the existence and uniqueness of the approximate solutions. The analysis provided here is not limited to specific reaction functions, and it is applicable to all conforming and non-conforming schemes fitting within the GDM framework. As an application, we present numerical results based on a finite volume method.