论文标题
参数 - 均匀的近似值，对于不连续的初始条件，奇异的对流扩散问题
Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition
论文作者
论文摘要
检查了具有不连续初始条件的对流扩散类型的奇异扰动抛物线问题。确定了特定的免费误差函数，该函数与初始条件下的不连续性匹配。该分析函数与抛物线问题解决方案之间的差异是数值近似的。使用坐标转换，以便可以将层拟合的网格对齐到解决方案中的内层。为关联的数值方法提供了数值分析，该方法确定数值方法是一种参数均匀的数值方法。提出了数值结果，以说明论文中建立的重点误差界限。
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.
