In this article, we study some anisotropic singular perturbations for a class of linear elliptic problems. A uniform estimates for conforming $Q_1$ finite element method are derived, and some other results of convergence and regularity for the continuous problem are proved.

翻译：本文研究一类线性椭圆问题的各向异性奇异摄动。推导了协调$Q_1$有限元方法的一致估计，并证明了连续问题的一些收敛性和正则性结果。