We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a convergence analysis on layer adapted meshes and an optimal convergence order in a balanced norm that is comparable with a balanced $H^2$-norm for the second order formulation.

翻译：我们认为一个异常扰动的反应扩散问题是一个二乘二的系统。 在第一个组件中,我们使用片断不连续的多元分子元素,在第二个组件中则使用$H ⁇ div}($H ⁇ div})与美元相符元素,我们提供了对经调整的甲草胺层的趋同分析,以及一种平衡的统合秩序,该规范与第二序列配方的平衡值相仿。