For a reaction-dominated diffusion problem we study a primal and a dual hybrid finite element method where weak continuity conditions are enforced by Lagrange multipliers. Uniform robustness of the discrete methods is achieved by enriching the local discretization spaces with modified face bubble functions which decay exponentially in the interior of an element depending on the ratio of the singular perturbation parameter and the local mesh-size. A posteriori error estimators are derived using Fortin operators. They are robust with respect to the singular perturbation parameter. Numerical experiments are presented that show that oscillations, if present, are significantly smaller then those observed in common finite element methods.

翻译：针对反应主导扩散问题，我们研究了一种原始混合和一种对偶混合有限元方法，其中通过拉格朗日乘子施加弱连续性条件。通过在局部离散化空间中添加修正的面泡函数，实现了离散方法的统一鲁棒性，这些函数根据奇异摄动参数与局部网格尺寸的比值在单元内部呈指数衰减。利用Fortin算子推导了后验误差估计子，该估计子对奇异摄动参数具有鲁棒性。数值实验表明，若存在振荡，其幅度明显小于常规有限元方法中观测到的振荡。