A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The difference between this analytical function and the solution of the parabolic problem is approximated numerically. A co-ordinate transformation is used so that a layer-adapted mesh can be aligned to the interior layer present in the solution. Numerical analysis is presented for the associated numerical method, which establishes that the numerical method is a parameter-uniform numerical method. Numerical results are presented to illustrate the pointwise error bounds established in the paper.

中文翻译：

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具有不连续初始条件的奇异扰动对流扩散问题的参数一致近似

研究了具有不连续初始条件的对流扩散类型的奇异摄动抛物线问题。识别出与初始条件中的不连续性相匹配的特定互补误差函数。该解析函数与抛物线问题的解之间的差异在数值上是近似的。使用坐标变换，以便层适应网格可以与解决方案中存在的内部层对齐。对相关数值方法进行了数值分析，确定该数值方法是参数一致的数值方法。给出了数值结果来说明论文中建立的逐点误差界限。