In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating this model using both conforming and non conforming discretisation methods. Under standard assumptions on the time discretisation, we establish the existence and uniqueness of the discrete solution. Numerical experiments are conducted using a mixed finite volume scheme that fits within the proposed unified framework. A test case with an analytical solution is designed to confirm our theoretical convergence rates.

翻译：本文研究了一类模拟生物膜生长的带约束抛物型反应-扩散系统。在一个包含多种数值格式的统一框架内，我们首次推导了使用协调与非协调离散化方法逼近该模型的通用收敛速率。在时间离散化的标准假设下，我们证明了离散解的存在唯一性。通过采用符合所提统一框架的混合有限体积格式进行数值实验，并设计了具有解析解的测试案例以验证理论收敛速率。