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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >A robust method of improved order for convection-diffusion problems in a domain with characteristic boundaries
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A robust method of improved order for convection-diffusion problems in a domain with characteristic boundaries

机译：具有特征边界的区域中对流扩散问题的改进阶数的鲁棒方法

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摘要

We consider a singularly perturbed two-dimensional convection-diffusion problem in a rectangle with flow parallel to the x-axis. On the inflow and outflow boundaries Dirichlet type conditions are. imposed and on. the characteristic boundaries regular Robin type conditions (including the possibility of Neumann conditions) are given. For small values of the parameter epsilon, regular (strong) and parabolic (weak) layers appear. In this case the parabolic layers do not involve the first term of the asymptotic expansion. For the proposed problem, epsilon-uniformly convergent methods are considered. Note, that for the upwind finite difference scheme the order of epsilon-uniform convergence does not exceed one. Using the High Order Compact (HOC) standard technique, we construct a classical method on piecewise uniform Shishkin meshes having uniform convergence with order 3/2 in the maximum norm. Numerical results are presented and discussed. [References: 22]
机译：我们考虑流动平行于x轴的矩形中的奇摄动二维对流扩散问题。在流入和流出边界上Dirichlet类型条件是。施加和继续。给出了常规罗宾型条件（包括诺伊曼条件的可能性）的特征边界。对于较小的参数ε，将显示常规（强）层和抛物线（弱）层。在这种情况下，抛物线层不涉及渐近展开的第一项。对于提出的问题，考虑了ε均匀收敛方法。注意，对于迎风有限差分方案，ε均匀收敛的阶数不超过1。使用高阶紧凑（HOC）标准技术，我们对分段均匀的Shishkin网格构造了一种经典方法，该网格具有在最大范数中具有3/2阶的均匀收敛性。提出并讨论了数值结果。 [参考：22]

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