In this paper, we present a novel 1D singularly perturbed reaction–convection–diffusion mathematical model, with non-linear coefficients (SP-RCD model), for the physical modeling of a fuel cell. The model is a generalization of the macro-homogeneous model, revisited from the point of view of singularly perturbed differential equations. To solve the system of coupled second-order differential equations, we propose a numerical scheme based on vanishing the artificial diffusion of the finite element method within an iterative fixed-point algorithm. We also propose an adaptive Shishkin mesh, as a function of the derivative of the current density in the subdomain with a fast-growing slope. Results of the proposed SP-RCD model are comparable to those of the macro-homogeneous model. In addition, it describes the oxygen concentration profiles in the thickness of the cathode catalytic layer under different operating currents and represents, with enough precision, the experimental polarization curve reported in the literature.

在本文中，我们提出了一种具有非线性系数的新型一维奇异扰动反应-对流-扩散数学模型（SP-RCD 模型），用于燃料电池的物理建模。该模型是宏观齐次模型的推广，从奇异摄动微分方程的角度重新审视。为了求解耦合二阶微分方程组，我们提出了一种基于在迭代定点算法中消除有限元方法的人工扩散的数值方案。我们还提出了一种自适应 Shishkin 网格，它是具有快速增长斜率的子域中电流密度导数的函数。提出的 SP-RCD 模型的结果与宏观均匀模型的结果相当。此外，