In this paper, we investigate adaptive streamline upwind/Petrov Galerkin (SUPG) methods for second order convection-diffusion-reaction equations with singular perturbation in a new dual norm presented in [17]. The flux can be recovered in two different manners: local averaging in conforming $H(\mathrm{div})$ spaces, and weighted global $L^2$ projection onto conforming $H(\mathrm{div})$ spaces. We further propose a recovery stabilization procedure, and provide completely robust a posteriori error estimators with respect to the singular perturbation parameter ε. Numerical experiments are provided to confirm theoretical results and to show that the estimated errors depend on the degrees of freedom uniformly in the diffusion parameter ε.

在本文中，我们研究了自适应流线迎风/彼得罗夫伽辽金 (SUPG) 方法，用于在 [17] 中提出的新对偶范数中具有奇异扰动的二阶对流-扩散-反应方程。通量可以通过两种不同的方式恢复：局部平均$H(\mathrm{div})$ 空间和加权全局 ${升}^2$ 投影到符合 $H(\mathrm{div})$空间。我们进一步提出了恢复稳定程序，并提供了关于奇异扰动参数ε 的完全稳健的后验误差估计器。提供了数值实验以确认理论结果并表明估计误差均匀地取决于扩散参数ε 中的自由度。