In this paper, a second-order local and parallel space-time algorithm is proposed and analyzed for the heat equation. This scheme is based on the parareal with spectral deferred correction method in time and the expandable local and parallel finite element method in space. It realizes the parallelism both in the temporal as well as in the spatial direction. We prove its stability and the optimal error estimation in $L^2$-norm. At last, several numerical experiments are presented to demonstrate the effectiveness of our parallel scheme.

中文翻译：

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热方程的局部并行时空算法分析

本文提出并分析了热方程的二阶局部并行时空算法。该方案基于时间上的带谱延迟校正的parareal方法和空间上可扩展的局部并行有限元方法。它实现了时间和空间方向的并行性。我们证明了它的稳定性和最优误差估计${升}^2$-规范。最后，提出了几个数值实验来证明我们的并行方案的有效性。