低常规数据分散扩散问题的时间光谱方法的最佳误差估计最佳误差估计 (Optimal error estimation of a time-spectral method for fractional diffusion problems with low regularity data)

This paper is devoted to the error analysis of a time-spectral algorithm for fractional diffusion problems of order $\alpha$ ($0 < \alpha < 1$). The solution regularity in the Sobolev space is revisited, and new regularity results in the Besov space are established. A time-spectral algorithm is developed which adopts a standard spectral method and a conforming linear finite element method for temporal and spatial discretizations, respectively. Optimal error estimates are derived with nonsmooth data. Particularly, a sharp temporal convergence rate $1+2\alpha$ is shown theoretically and numerically.

翻译：本文专门论述对时间光谱算法的错误分析,该算法用于分析单位扩散问题($\alpha$(0 < αpha < 1美元))的分位扩散问题。索博列夫空间的溶解规律性得到重新审视,贝索夫空间的新的规律性结果得到确定。开发了时间光谱算法,分别采用标准光谱法和符合的线性有限元素法,用于时间和空间分解。最佳误差估计是用非光学数据得出的。特别是,从理论上和数字上显示了急剧的时间趋同率1+2\阿尔法元。