论文标题
在某些有限差方方案的稳定边界封闭中
On some stable boundary closures of finite difference schemes for the transport equation
论文作者
论文摘要
我们在本文中探讨了所谓的能量方法的可能性和局限性，用于分析有限差近似于传输方程的稳定性，并在流出边界外推外数值边界条件。我们首先表明，对于最简单的方案，即带有三点模具的显式方案，可以将能量方法用于证明稳定性估计的稳定性估计是在使用第一阶或二阶外推边界条件实现该方案时。然后，我们检查了五个点模板的情况，并给出了几个方案的例子和二阶外推数值边界条件，能量方法会产生稳定性估计。但是，我们还表明，对于标准的一阶或二阶译动推断外推边界条件，不能应用能量方法来证明最初由Strang提出的经典第四阶方案的稳定性。这对基于正常模式分解的更通用方法的能量法明确局限。
We explore in this article the possibilities and limitations of the so-called energy method for analyzing the stability of finite difference approximations to the transport equation with extrapolation numerical boundary conditions at the outflow boundary. We first show that for the most simple schemes, namely the explicit schemes with a three point stencil, the energy method can be applied for proving stability estimates when the scheme is implemented with either the first or second order extrapolation boundary condition. We then examine the case of five point stencils and give several examples of schemes and second order extrapolation numerical boundary conditions for which the energy method produces stability estimates. However, we also show that for the standard first or second order translatory extrapolation boundary conditions, the energy method cannot be applied for proving stability of the classical fourth order scheme originally proposed by Strang. This gives a clear limitation of the energy method with respect to the more general approach based on the normal mode decomposition.
