We discuss the superconvergence analysis of the Galerkin finite element method for the singularly perturbed coupled system of both reaction–diffusion and convection–diffusion types. The superconvergence study is carried out by using linear finite element, and it is shown to be second-order (up to a logarithmic factor) uniformly convergent in the suitable discrete energy norm. We have conducted some numerical experiments for the system of reaction–diffusion and system of convection–diffusion models, which validate the theoretical results.

中文翻译：

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多尺度自然奇摄动系统Galerkin有限元超收敛分析的统一研究

我们讨论了Galerkin有限元方法对反应扩散和对流扩散类型的奇摄动耦合系统的超收敛性分析。超收敛研究是通过使用线性有限元进行的，它被证明是二阶（直到对数因子）在合适的离散能量范数下均匀收敛。我们对反应扩散系统和对流扩散模型系统进行了一些数值实验，验证了理论结果。