论文标题
格林对2D奇异扰动对流扩散问题的功能估计：扩展分析
Green's function estimates for a 2d singularly perturbed convection-diffusion problem: extended analysis
论文作者
论文摘要
本文介绍了该文章的扩展版本[Franz，S.，Kopteva，n。：J。Interial方程，252（2012）]。与后者相比，主要的改进是，在这里我们还估计了绿色功能的混合二阶导数。还解决了沿特征边界的诺伊曼条件的情况。在单位正方形中带有水平对流方向的单位正方形提出了一个奇异的扰动对流扩散问题。它的解决方案表现出抛物线和指数边界层。对绿色功能及其一阶和二阶导数的敏锐估计是在$ L_1 $规范中得出的。这些估计值对小扩散参数的依赖性被明确显示。所获得的估计值将用于对所考虑问题的即将进行的数值分析。
This paper presents an extended version of the article [Franz, S., Kopteva, N.: J. Differential Equations, 252 (2012)]. The main improvement compared to the latter is in that here we additionally estimate the mixed second-order derivative of the Green's function. The case of Neumann conditions along the characteristic boundaries is also addressed. A singularly perturbed convection-diffusion problem is posed in the unit square with a horizontal convective direction. Its solutions exhibit parabolic and exponential boundary layers. Sharp estimates of the Green's function and its first- and second-order derivatives are derived in the $L_1$ norm. The dependence of these estimates on the small diffusion parameter is shown explicitly. The obtained estimates will be used in a forthcoming numerical analysis of the considered problem.
