论文标题
与不连续的初始条件的奇异扰动对流扩散问题的数值近似
Numerical approximations to 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。确定了与初始条件中的不连续性相匹配的分析函数，并且还满足与问题相关的均质抛物线微分方程。这种分析函数和抛物线问题解决方案之间的差异是在数值上近似的，使用上风有限差算子与适当的层适应网格结合使用。数值方法显示为参数均匀。提出了数值结果，以说明论文中建立的理论误差界限。
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.
