We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit boundary layers as well as weak interior layers. A numerical method based on finite element method (Shishkin and Bakhvalov-Shishkin meshes) is presented. We derive an error estimate of order $O(N^{-1}\ln^{3/2}{N})$ in the energy norm with respect to the perturbation parameter. Numerical experiments are also presented to support our theoretical results.

翻译：我们认为一种系统是两种单一扰动的边界值问题(BVPs),一种是源值不连续的对流扩散型,一种是乘以最高衍生物的微小正参数。然后,它们的解决方案显示边界层以及薄弱的内部层。提出了一种基于有限元素方法的数字方法(Shishkin和Bakhvalov-Shishkin meshes)。我们从能源标准中得出关于扰动参数的美元(N ⁇ -1 ⁇ ln ⁇ 3/2 ⁇ N})顺序的误差估计。还提出了数字实验,以支持我们的理论结果。