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.
翻译:检查了异常扰动的对流-扩散类型的抛物线问题,最初状态不连续。确定了一种与初始状态不连续相匹配的特殊互补错误函数。该分析函数与抛物线问题解决方案的差别在数字上大致相同。使用了一个坐标变换,使图层适应的网格能够与解决方案中存在的内层对齐。为相关数字方法提供了数值分析,该方法确定数字方法是一种参数-统一的数字方法。提供了数字结果,以说明文件中设定的点误差界限。