A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the homogenous parabolic differential equation associated with the problem. The difference between this analytical function and the solution of the parabolic problem is approximated numerically, using an upwind finite difference operator combined with an appropriate layer-adapted mesh. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established in the paper.
翻译:检查了单一受扰动的对流-扩散类型的抛物线问题,最初状态不连续,初始状态不连续,初始状态不连续,分析功能与之相匹配,也满足了与问题相关的同质抛物线差异方程式。这一分析函数与抛物线问题解决办法之间的差别,用数字相近,使用上风的有限差异运算器,加上一个适合图层调整的适当网格。数字方法显示为参数单形。数字结果显示为数字结果,以说明文件中设定的理论错误界限。