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<p>This paper establishes the 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 solution under a small time discretisation. The analysis provided here is not limited to specific reaction functions and applies to all conforming and non-conforming schemes within the GDM framework. As an application, we present numerical results based on a finite volume method.</p>

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General error estimates of non-conforming approximation of system of reaction–diffusion equations

  • 期刊论文

  • 发表日期：

    2025年10月10日

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  • Yahya Alnashri

摘要

This paper establishes the 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 solution under a small time discretisation. The analysis provided here is not limited to specific reaction functions and applies to all conforming and non-conforming schemes within the GDM framework. As an application, we present numerical results based on a finite volume method.