We consider a class of singularly perturbed degenerate parabolic convection–diffusion problems on a rectangular domain. A numerical method is constructed using the implicit Euler scheme on a uniform mesh in the time direction and the upwind finite difference scheme on a layer adaptive non-uniform mesh in the spatial direction. The layer adaptive non-uniform mesh in the spatial direction is generated through the equidistribution of a suitably chosen monitor function. We perform error analysis through the truncation error and barrier function approach and prove that the method is uniformly convergent with first order in both time and space. Numerical results are given in support of theoretical findings.

我们考虑了矩形域上的一类奇摄动退化的抛物对流扩散问题。在时间方向上对均匀网格使用隐式欧拉方案，在空间方向上对层自适应非均匀网格使用迎风有限差分方案，构造了一种数值方法。在空间方向上的层的自适应非均匀网格是通过适当选择的监视功能的等分布生成。我们通过截断误差和势垒函数方法进行了误差分析，证明了该方法在时间和空间上均与一阶收敛。给出数值结果以支持理论发现。