论文标题
结构感知帐篷的泰勒方法的稳定性
Stability of structure-aware Taylor methods for tents
论文作者
论文摘要
结构感知的泰勒（SAT）方法是一类时间播放方案，旨在在帐篷形时区域内传播线性双曲线溶液。帐篷对于设计明确的时间行进方案在非结构化前进的前沿，内置可变的时间播放时间编程，以进行任意空间和时间离散订单。本文的主要结果是，在时间步长约束$ΔT\ leq ch^{1+1/s} $的情况下，帐篷内的$ s $ stage stage sat timespeppeptions在帐篷内进行了弱稳定，其中$ΔT$是时间步长，$ h $是空间网格大小。还提出了改进的稳定性特性，用于高阶SAT时间离散以及低阶空间多项式。还包括对验证估计的清晰度的数值验证。
Structure-aware Taylor (SAT) methods are a class of timestepping schemes designed for propagating linear hyperbolic solutions within a tent-shaped spacetime region. Tents are useful to design explicit time marching schemes on unstructured advancing fronts with built-in locally variable timestepping for arbitrary spatial and temporal discretization orders. The main result of this paper is that an $s$-stage SAT timestepping within a tent is weakly stable under the time step constraint $Δt \leq Ch^{1+1/s}$, where $Δt$ is the time step size and $h$ is the spatial mesh size. Improved stability properties are also presented for high order SAT time discretizations coupled with low order spatial polynomials. A numerical verification of the sharpness of proven estimates is also included.
